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References

Published online by Cambridge University Press:  05 July 2014

Giancarlo Travaglini
Giancarlo Travaglini
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Università degli Studi di Milano-Bicocca
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Number Theory, Fourier Analysis and Geometric Discrepancy , pp. 229 - 237
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Print publication year: 2014

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References

[1] T. van, Aardenne-Ehrenfest, Proof of the impossibility of a just distribution of an infinite sequence of points over an interval, Proc. Kon. Ned. Akad. v. Wetensch 48 (1945), 266–271.Google Scholar
[2] T. van, Aardenne-Ehrenfest, On the impossibility of a just distribution, Proc. Kon. Ned. Akad. v. Wetensch 52 (1949), 734–739.Google Scholar
[3] W.W., Adams, L.J., Goldstein, Introduction to number theory, Prentice-Hall, 1976.Google Scholar
[4] J., Agnew, Explorations in number theory, Contemporary Undergraduate Mathematics Series, Brooks/Cole, 1972.Google Scholar
[5] W.R., Alford, A., Granville, C., Pomerance, There are infinitely many Carmichael numbers, Ann. of Math. 139 (1994), 703–722.Google Scholar
[6] G.E., Andrews, Number theory, Dover Publications, 1994.Google Scholar
[7] G.E., Andrews, S.B., Ekhad, D., Zeilberger, A Short Proof of Jacobi's formula for the number of representations of an integer as a sum of four squares, Amer. Math. Monthly 100 (1993), 274–276.Google Scholar
[8] T.M., Apostol, Introduction to analytic number theory, Undergraduate Texts in Mathematics, Springer, 1998.Google Scholar
[9] A., Baker, A concise introduction to the theory of numbers, Cambridge University Press, 1984.Google Scholar
[10] P.T., Bateman, H.G., Diamond, Analytic number theory. An introductory course, World Scientific Publishing, 2004.Google Scholar
[11] D., Bayer, P., Diaconis, Trailing the dovetail shuffle to its lair, Ann. Appl. Probab. 2 (1992), 294–313.Google Scholar
[12] J., Beck, Balanced two-colourings of finite sets in the square I, Combinatorica 1 (1981), 50–64.Google Scholar
[13] J., Beck, Irregularities of distribution I, Acta Math. 159 (1987), 1–49.Google Scholar
[14] J., Beck, W.W.L., Chen, Irregularities of distribution, Cambridge Tracts in Mathematics, 89, Cambridge University Press, 2008.Google Scholar
[15] J., Beck, W.W.L., Chen, Note on irregularities of distribution II, Proc. London Math. Soc. 61 (1990), 251–272.Google Scholar
[16] D.R., Bellhouse, Area estimation by point counting techniques, Biometrics 37 (1981), 303–312.Google Scholar
[17] F., Benford, The law of anomalous numbers, Proc. Am. Philos. Soc. 78 (1938), 551–572.Google Scholar
[18] A., Berger, T.P., Hill, Benford's law strikes back: no simple explanation in sight for mathematical gem, Math. Intelligencer 33 (2011), 85–91.Google Scholar
[19] D., Bilyk, Roth's orthogonal functions method in discrepancy theory and some new connections, in ‘A panorama of discrepancy theory’ (W.W.L., Chen, A., Sri-vastav, G., Travaglini - Editors), Lecture Notes in Mathematics, Springer, to appear.
[20] S., Bochner, The role of mathematics in the rise of science, Princeton University Press, 1966.Google Scholar
[21] E., Borel, Les probabilités denombrables et leurs applications arithmétiques, Rend. Circ. Mat. Palermo 27 (1909), 247–271.Google Scholar
[22] L., Brandolini, W.W.L., Chen, L., Colzani, G., Gigante, G., Travaglini, Discrepancy and numerical integration in Sobolev spaces on metric measures spaces, preprint.
[23] L., Brandolini, W.W.L., Chen, G., Gigante, G., Travaglini, Discrepancy for randomized Riemann sums, Proc. Amer. Math. Soc. 137 (2009), 3177–3185.Google Scholar
[24] L., Brandolini, C., Choirat, L., Colzani, G., Gigante, R., Seri, G., Travaglini, Quadrature rules and distribution of points on manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci., to appear
[25] L., Brandolini, L., Colzani, G., Gigante, G., Travaglini, On the Koksma-Hlawka inequality, J. Complexity 29 (2013), 158–172.Google Scholar
[26] L., Brandolini, L., Colzani, G., Gigante, G., Travaglini, A Koksma-Hlawka inequality for simplices, in ‘Trends in harmonic analysis’ (M., Picardello - Editor), Springer INd AM Series, Springer, 2013, 33–46.Google Scholar
[27] L., Brandolini, L., Colzani, A., Iosevich, A., Podkorytov, G., Travaglini, Geometry of the Gauss map and lattice points in convex domains, Mathematika 48 (2001), 107–117.Google Scholar
[28] L., Brandolini, L., Colzani, G., Travaglini, Average decay of Fourier transforms and integer points in polyhedra, Ark. Mat. 35 (1997), 253–275.Google Scholar
[29] L., Brandolini, G., Gigante, S., Thangavelu, G., Travaglini, Convolution operators deined by singular measures on the motion group, Indiana Univ. Math. J. 59 (2010), 1935–1945.Google Scholar
[30] L., Brandolini, G., Gigante, G., Travaglini, Irregularities of distribution and average decay of Fourier transforms, in ‘A panorama of discrepancy theory’ (W.W.L., Chen, A., Srivastav, G., Travaglini – Editors), Lecture Notes in Mathematics, Springer, to appear
[31] L., Brandolini, A., Greenleaf, G., Travaglini, Lp – Lp′ estimates for overdetermined Radon transforms, Trans. Amer. Math. Soc. 359 (2007), 2559–2575.Google Scholar
[32] L., Brandolini, S., Hofmann, A., Iosevich, Sharp rate of average decay of the Fourier transform of a bounded set, Geom. Funct. Anal. 13 (2003), 671–680.Google Scholar
[33] L., Brandolini, A., Iosevich, G., Travaglini, Spherical means and the restriction phenomenon, J. Fourier Anal. Appl. 7 (2001), 359–372.Google Scholar
[34] L., Brandolini, A., Iosevich, G., Travaglini, Planar convex bodies, Fourier transform, lattice points, and irregularities of distribution, Trans. Amer. Math. Soc. 355 (2003), 3513–3535.Google Scholar
[35] L., Brandolini, M., Rigoli, G., Travaglini, Average decay of Fourier transforms and geometry ofconvexsets, Rev. Mat. Iberoamer. 14 (1998), 519–560.Google Scholar
[36] L., Brandolini, G., Travaglini, Pointwise convergence of Fejér type means, Tohoku Math. J. 49 (1997), 323–336.Google Scholar
[37] L., Brandolini, G., Travaglini, La legge di Benford, Emmeciquadro 45 (2012).Google Scholar
[38] J., Bruna, A., Nagel, S., Wainger, Convex hypersurfaces and Fourier transforms, Ann. of Math. 127 (1988), 333–365.Google Scholar
[39] F., Cantelli, Sulla probabilità come limite della frequenza, Atti Accad. Naz. Lincei 26 (1917), 39–45.Google Scholar
[40] J.W.S., Cassels, On the sums of powers of complexnumbers, Acta Math. Hungar. 7 (1957), 283–289.Google Scholar
[41] D.G., Champernowne, The construction of decimal normal in the scale of ten, J. London Math. Soc. 8 (1933), 254–260.Google Scholar
[42] K., Chandrasekharan, Introduction to analytic number theory, Die Grundlehren der mathematischen Wissenschaften, Band 148, Springer, 1968.Google Scholar
[43] B., Chazelle, The discrepancy method. Randomness and complexity, Cambridge University Press, 2000.Google Scholar
[44] W.W.L., Chen, On irregularities of distribution III, J. Austr. Math. Soc. 60 (1996), 228–244.Google Scholar
[45] W.W.L., Chen, Lectures on irregularities of point distribution, unpublished, 2000.Google Scholar
[46] W.W.L., Chen, Elementary number theory, unpublished, 2003.Google Scholar
[47] W.W.L., Chen, Fourier techniques in the theory of irregularities of point distribution, in ‘Fourier analysis and convexity’ (L., Brandolini, L., Colzani, A., Iosevich, G., Travaglini - Editors), Birkhauser, 2004, 59–82.Google Scholar
[48] W.W.L., Chen, M., Skriganov, Upper bounds in irregularities of point distribution, in “Apanorama of discrepancy theory” (W.W.L., Chen, A., Srivastav, G., Travaglini – Editors), Lecture Notes in Mathematics, Springer, to appear.
[49] W.W.L., Chen, A., Srivastav, G., Travaglini - Editors, A panorama of discrepancy theory, Lecture Notes in Mathematics, Springer, to appear.
[50] W.W.L., Chen, G., Travaglini, Discrepancy with respect to convex polygons, J. Complexity 23 (2007), 662–672.Google Scholar
[51] W.W.L., Chen, G., Travaglini, Deterministic and probabilistic discrepancies, Ark. Mat. 47 (2009), 273–293.Google Scholar
[52] W.W.L., Chen, G., Travaglini, Some of Roth's ideas in discrepancy theory, in ‘Analytic number theory: essays in honour of Klaus Roth’ (W.W.L., Chen, W.T., Gowers, H., Halberstam, W.M., Schmidt, R.C., Vaughan – Editors), Cambridge University Press, 2009, 150–163.Google Scholar
[53] P.R., Chernoff, Pointwise convergence of Fourier series, Amer. Math. Monthly 87 (1980),399–400.Google Scholar
[54] K.L., Chung, A course in probability theory, Academic Press, 2001.Google Scholar
[55] M., Cipolla, Sui numeri composti Pcheveriicano la congruenza di Fermat ap-1 ≡ 1 (mod P), Ann. Mat. Pura Appl. 9 (1904), 139–160.Google Scholar
[56] J.A., Clarkson, On the series of prime reciprocals, Proc. Amer. Math. Soc. 17 (1966), 541.Google Scholar
[57] L., Colzani, G., Gigante, Summation formulas and integer points under shifted generalized hyperbolae, preprint.
[58] L., Colzani, G., Gigante, G., Travaglini, Trigonometric approximation and a general form of the Erdos-Turán inequality, Trans. Amer. Math. Soc. 363 (2011), 1101–1123.Google Scholar
[59] L., Colzani, G., Gigante, G., Travaglini, Unpublished, 2012.Google Scholar
[60] L., Colzani, I., Rocco, G., Travaglini, Quadratic estimates for the number of integer points in convex bodies, Rend. Circ. Mat. Palermo 54 (2005), 241–252.Google Scholar
[61] J.H., Conway, R.K., Guy, The book of numbers, Copernicus, 1996.Google Scholar
[62] A.H., Copeland, P., Erdos, Note on normal numbers, Bull. Amer. Math. Soc. 52 (1946), 857–860.Google Scholar
[63] W.A., Coppel, Number theory. An introduction to mathematics, Springer, 2009.Google Scholar
[64] J.G. van der, Corput, Zalhentheorische abschätzungen, Math. Ann. 84 (1921), 53–79.Google Scholar
[65] J.G. van der, Corput, Zalhentheorische abschätzungen mit anwendung auf gitter-punktprobleme, Math. Z. 17 (1923), 250–259.Google Scholar
[66] J.G. van der, Corput, Verteilungsfunktionen I-VIII, Proc. Akad. Amsterdam 38 (1935), 813–821, 1058-1066; 39 (1936), 10-19, 19-26, 149-153, 339-344, 489-494, 579-590.Google Scholar
[67] H., Davenport, Notes on irregularities of distribution, Mathematika 3 (1956), 131–135.Google Scholar
[68] J. De, Koninck, F., Luca, Analytic number theory. Exploring the anatomy of integers. Graduate Studies in Mathematics, 134, American Mathematical Society, 2012.Google Scholar
[69] P., Diaconis, The distribution of leading digits and uniform distribution mod 1, Ann. Prob. 5 (1977), 72–81.Google Scholar
[70] P., Diaconis, D., Freedman, On rounding percentages, J. Amer. Statist. Assoc. 366 (1979), 359–364.Google Scholar
[71] J., Dick, F., Pillichshammer, Discrepancy theory and quasi-Monte Carlo integration, in ‘A panorama of discrepancy theory’ (W.W.L., Chen, A., Srivastav, G., Travaglini – Editors), Lecture Notes in Mathematics, Springer, to appear.
[72] L.E., Dickson, History of the theory of numbers, Vol. I, II, Chelsea Publishing Co., 1966.Google Scholar
[73] M., Drmota, R.F., Tichy, Sequences, discrepancies and applications. Lecture Notes in Mathematics, 1651, Springer, 1997.Google Scholar
[74] P., Erdos, On almost primes, Amer. Math. Monthly 57 (1950), 404–407.Google Scholar
[75] P., Erdos, W.H.J., Fuchs, On a problem of additive number theory, J. London Math. Soc. 31 (1956), 67–73.Google Scholar
[76] P., Erdos, J., Suranyi, Topics in the theory of numbers, Undergraduate Texts in Mathematics, Springer, 2003.Google Scholar
[77] P., Erdos, P., Turan, On a problem in the theory of uniform distribution I, II, Indag. Math. 10 (1948), 370-378, 406–413.Google Scholar
[78] G., Everest, T., Ward, An introduction to number theory, Graduate Texts in Mathematics, 232, Springer, 2005.Google Scholar
[79] D.E., Flath, Introduction to number theory, John Wiley & Sons, 1989.Google Scholar
[80] B., Flehinger, On the probability that a random integer has initial digit A, Amer. Math. Monthly 73 (1966), 1056–1061.Google Scholar
[81] G.B., Folland, Fourier analysis and its applications, Wadsworth & Brooks/Cole, 1992.Google Scholar
[82] G.B., Folland, Real analysis. Modern techniques and their applications, John Wiley & Sons, 1999.Google Scholar
[83] L.J., Goldstein, A history of the prime number theorem, Amer. Math. Monthly 80 (1973), 599–615.Google Scholar
[84] S.W., Graham, G., Kolesnik, Van der Corput's method of exponential sums, London Mathematical Society Lecture Note Series, 126, Cambridge University Press, 1991.Google Scholar
[85] A., Granville, The Fundamental theorem of arithmetic, preprint.
[86] A., Granville, Z., Rudnick – Editors, Equidistribution in number theory, an introduction, Springer, 2007
[87] T.H., Gronwall, Some asymptotic expressions in the theory of numbers, Trans. Amer. Math. Soc. 14 (1913), 113–122.Google Scholar
[88] G.H., Hardy, On the expression of a number as the sum of two squares, Quart. J. Math. 46 (1915), 263–283.Google Scholar
[89] G.H., Hardy, On Dirichlet's divisor problem, Proc. London Math. Soc. 15 (1916), 1–25.Google Scholar
[90] G.H., Hardy, E.M., Wright, An introduction to the theory of numbers, Oxford University Press, 1938.Google Scholar
[91] G., Harman, Metric number theory, London Mathematical Society Monographs, New Series, 18, Oxford University Press, 1998.Google Scholar
[92] G., Harman, Variations on the Koksma-Hlawka inequality, Unif. Distr. Theory 5 (2010), 65–78.Google Scholar
[93] H., Hasse, Number theory, Springer, 1980.Google Scholar
[94] F.J., Hickernell, Koksma-Hlawka inequality, in ‘Encyclopedia of statistical sciences’ (S., Kotz, C.B., Read, D.L., Banks - Editors), Wiley-Interscience, 2006.Google Scholar
[95] E., Hlawka, The theory of uniform distribution, AB Academic Publishers, 1984.Google Scholar
[96] E., Hlawka, J., Schoißengeier, R., Taschner, Geometric and analytic number theory, Universitext, Springer, 1991.Google Scholar
[97] P., Hoffman, The man who loved only numbers: The story of Paul Erdos and the search for mathematical truth, Hyperion Books, 1998.Google Scholar
[98] L.K., Hua, Introduction to number theory, Springer, 1982.Google Scholar
[99] M.N., Huxley, The mean lattice point discrepancy, Proc. Edinburgh Math. Soc. 38 (1995), 523–531.Google Scholar
[100] M.N., Huxley, Area, lattice points and exponential sums, London Mathematical Society Monographs, New Series, 13, Oxford Science Publications, 1996.Google Scholar
[101] K., Ireland, M., Rosen, A classical introduction to modern number theory, Graduate Texts in Mathematics, 84, Springer, 1990.Google Scholar
[102] A., Ivic, The Riemann zeta-function. Theory and applications, Dover Publications, 2003.Google Scholar
[103] G.A., Jones, J.M., Jones, Elementary number theory, Springer Undergraduate Mathematics Series, Springer, 1998.Google Scholar
[104] C., Joy, P.P., Boyle, K.S., Tan, Quasi-Monte Carlo methods in inance, Management Science 42 (1996), 926–938.Google Scholar
[105] Y., Katznelson, An introduction to harmonic analysis, Cambridge Mathematical Library, Cambridge University Press, 2004.Google Scholar
[106] D.G., Kendall, On the number of lattice points in a random oval, Quart. J. Math. Oxford Series 19 (1948), 1–26.Google Scholar
[107] N., Koblitz, A course in number theory and cryptography, Graduate Texts in Mathematics, 114, Springer, 1994.Google Scholar
[108] H., Koch, Number theory, Graduate Studies in Mathematics, American Mathematical Society, 2000.Google Scholar
[109] J.F., Koksma, Een algemeene stellinguit de theorie der gelijkmatige verdeeling modulo 1, Mathematica B (Zupten) 11 (1942–43), 7–11.Google Scholar
[110] T., Kollig, A., Keller, Efficient multidimensional sampling, Computer Graphics Forum 21 (2002), 557–563.Google Scholar
[111] M.N., Kolountzakis, T., Wolff, On the Steinhaus tiling problem, Mathematika 46 (1999), 253–280.Google Scholar
[112] S.V., Konyagin, M.M., Skriganov, A.V., Sobolev, On a lattice point problem arising in the spectral analysis of periodic operators, Mathematika 50 (2003), 87–98.Google Scholar
[113] E., Kratzel, Lattice points, Mathematics and its Applications, Kluwer Academic Publisher, 1988.Google Scholar
[114] L., Kuipers, H., Niederreiter, Uniform distribution of sequences, Dover Publications, 2006.Google Scholar
[115] E., Landau, Über die gitterpunkte in einen kreise (Erste, zweite Mitteilung), Nachr. K. Gesellschaft Wiss. Gottingen, Math.-Phys. Klasse (1915), 148-160, 161–171.Google Scholar
[116] E., Landau, ber Dirichlets teilerproblem, Sitzungsber, Math.-Phys. Klasse Knigl. Bayer. Akad. Wiss. (1915), 317–328.Google Scholar
[117] N.N., Lebedev, Special functions and their applications, Dover Publication, 1972.Google Scholar
[118] F., Lemmermeyer, Reciprocity laws (from Euler to Eisenstein), Springer Monographs in Mathematics, Springer, 2000.Google Scholar
[119] W.J., LeVeque, Fundamentals of number theory, Addison-Wesley, 1977.Google Scholar
[120] W.J., LeVeque, Elementary theory of numbers, Dover Publications, 1990.Google Scholar
[121] J., Matousek, Geometric discrepancy. An illustrated guide, Algorithms and Combinatorics, 18, Springer, 2010.Google Scholar
[122] R., Matthews, The power of one, New Scientist, 10 July 1999.Google Scholar
[123] H., Montgomery, Ten lectures on the interface between analytic number theory and harmonic analysis, CBMS Regional Conference Series in Mathematics, 84, American Mathematical Society, 1994.Google Scholar
[124] W.J., Morokoff, R.E., Caflisch, A quasi-Monte Carlo approach to particle simulation of the heat equation, SIAM J. Numer. Anal. 30 (1993), 1558–1573.Google Scholar
[125] R.M., Murty, N., Thain, Prime numbers in certain arithmetic progressions, Funct. Approx. Comment. Math. 35 (2006), 249–259.Google Scholar
[126] R.M., Murty, N., Thain, Pick's theorem via Minkowski's theorem, Amer. Math. Monthly 114 (2007), 732–736.Google Scholar
[127] W., Narkiewicz, Number theory, World Scientific, 1983.Google Scholar
[128] M.B., Nathanson, Elementary methods in number theory, Graduate Texts in Mathematics, 195, Springer, 2000.Google Scholar
[129] S., Newcomb, Note on the frequency of use of the different digits in natural numbers, Amer. J. Math. 4 (1881), 39–40.Google Scholar
[130] D.J., Newman, A simplified proof of the Erdos-Fuchs theorem, Proc. Amer. Math. Soc. 75 (1979), 209–210.Google Scholar
[131] H., Niederreiter, Random number generation and quasi-Monte Carlo methods, CBMS-NSF Regional Conference Series in Applied Mathematics, 63, SIAM, 1992.Google Scholar
[132] M., Nigrini, Benford's law. Applications for forensic accounting, Auditing, and fraud detection, John Wiley & Sons, 2012.Google Scholar
[133] M., Nigrini, L., Mittermaier, The use of Benford's law as an aid in analytical procedures, Auditing – A Journal of Practice & Theory 16 (1997), 52–67.Google Scholar
[134] I., Niven, Irrational numbers, Carus Mathematical Monographs, 11, MAA, 2005.Google Scholar
[135] I., Niven, H., Zuckerman, An introduction to the theory of numbers, John Wiley & Sons, 1980.Google Scholar
[136] O., Ore, Number theory and its history, Dover Publications, 1988.Google Scholar
[137] L., Parnovski, N., Sidorova, Critical dimensions for counting lattice points in Euclidean annuli. Math. Model. Nat. Phenom. 5 (2010), 293–316.Google Scholar
[138] L., Parnovski, A., Sobolev, On the Bethe-Sommerfeld conjecture for the polyharmonic operator, Duke Math. J. 107 (2001), 209–238.Google Scholar
[139] R., Pinkham, On the distribution of first significant digits, Ann. Math. Stat. 32 (1961), 1223–1230.Google Scholar
[140] M.A., Pinsky, Introduction to Fourier analysis and wavelets, Graduate Studies in Mathematics, 102, American Mathematical Society, 2002.Google Scholar
[141] M., Plancherel, Contribution a l'etude de la representation d'une fonction arbitraire par les integrales definies, Rend. del Circ. Mat. Palermo 30 (1910), 298–335.Google Scholar
[142] A.N., Podkorytov, The asymptotic of a Fourier transform on a convex curve, Vestn. Leningr. Univ. Mat. 24 (1991), 57–65.Google Scholar
[143] S., Ramanujan, A proof of Bertrand's postulate, J. Indian Math. Soc. 11 (1919), 181–182.Google Scholar
[144] B., Randol, On the Fourier transform of the indicator function of a planar set, Trans. Amer. Math. Soc. 139, 271–278.
[145] D., Redmond, Number theory. An introduction, Monographs and Textbooks in Pure and Applied Mathematics, 201, Marcel Dekker, 1996.Google Scholar
[146] E., Regazzini, Probability and statistics in Italy during the First World War I: Cantelli and the laws of large numbers, J. Electron. Hist. Probab. Stat. 1 (2005) 1–12.Google Scholar
[147] F., Ricci, G., Travaglini, Convex curves, Radon transforms and convolution operators defined by singular measures, Proc. Amer. Math. Soc. 129 (2001), 1739–1744.Google Scholar
[148] S., Robinson, Still guarding secrets after years of attacks, RSA earns accolades for its founders, SIAM News 36 5 (2003).Google Scholar
[149] K.F., Roth, On irregularities of distribution, Mathematika 1 (1954), 73–79.Google Scholar
[150] W., Rudin, Principles of mathematical analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, 1976.Google Scholar
[151] J.D., Sally, P.J., Sally, Roots to research. A vertical development of mathematical problems, American Mathematical Society, 2007.Google Scholar
[152] W.M., Schmidt, Irregularities of distribution IV, Invent. Math. 7 (1968), 55–82.Google Scholar
[153] W.M., Schmidt, Lectures on irregularities of distribution, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 56, Tata Institute of Fundamental Research, Bombay, 1977.Google Scholar
[154] E., Scholz (Editor), Hermann Weyl's Raum-Zeit-Materie and a general introduction to his scientific work, DMV Seminar 30, Birkhauser, 2001.
[155] W., Sierpinski, O Pewnem zagadnieniu zrachunku funckcy asymptotycznych, Prace mat.-fiz. 17 (1906), 77–118.Google Scholar
[156] R.A., Silverman, Complex analysis with applications, Dover Publications, 1984.Google Scholar
[157] S., Singh, The code book: The science of secrecy from ancient Egypt to quantum cryptography, Doubleday Books, 1999.Google Scholar
[158] I.H., Sloan, H., Wozniakowski, When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?J. Complexity 14 (1998), 1–33.Google Scholar
[159] P., Soardi, Serie di Fourier in più variabili, Unione Matematica Italiana -Pitagora, Quaderni dell'Unione Matematica Italiana 26, 1984.
[160] C.D., Sogge, Fourier integrals in classical analysis, Cambridge Tracts in Mathematics, 105, Cambridge University Press, 1993.Google Scholar
[161] E., Stein, R., Shakarchi, Fourier analysis, An introduction, Princeton Lectures in Analysis, I, Princeton University Press, 2003.Google Scholar
[162] E., Stein, R., Shakarchi, Real analysis, Measure theory, integration, and Hilbert spaces, Princeton Lectures in Analysis, III, Princeton University Press, 2005.Google Scholar
[163] E., Stein, R., Shakarchi, Functional analysis, Princeton Lectures in Analysis IV, Princeton University Press, 2011.Google Scholar
[164] E., Stein, G., Weiss, Introduction to Fourier analysis in Euclidean spaces, Princeton Mathematical Series, 32, Princeton University Press, 1971.Google Scholar
[165] I.N., Stewart, D.O., Tall, Algebraic number theory, Chapman and Hall Mathematics Series, Chapman and Hall, 1979.Google Scholar
[166] J., Stillwell, Elements of algebra, Geometry, numbers, equations, Undergraduate Texts in Mathematics, Springer, 1994.Google Scholar
[167] J., Stillwell, Elements of number theory, Undergraduate Texts in Mathematics, Springer, 2003.Google Scholar
[168] D.R., Stinson, Cryptography, Theory and practice, CRC Press Series on Discrete Mathematics and its Applications, Chapman & Hall/CRC, 2002.Google Scholar
[169] M., Tarnopolska-Weiss, On the number of lattice points in planar domains, Proc. Amer. Math. Soc. 69 (1978), 308–311.Google Scholar
[170] G., Travaglini, Fejer kernels for Fourier series on Tn and on compact Lie groups, Math. Z. 216 (1994), 265–281.Google Scholar
[171] G., Travaglini, Crittograia, Emmeciquadro 21 (2004), 21–28.Google Scholar
[172] G., Travaglini, Average decay of the Fourier transform, in ‘Fourier analysis and convexity’ (L., Brandolini, L., Colzani, A., Iosevich, G., Travaglini – Editors), Birkhauser, 2004, 245–268.Google Scholar
[173] G., Travaglini, Appunti su teoria dei numeri, analisi di Fouriere distribuzione di punti, Unione Matematica Italiana – Pitagora, Quaderni dell'Unione Matematica Italiana 52, 2010.
[174] K., Tsang, Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function, Sci. China Math. 53 (2010), 2561–2572.Google Scholar
[175] M., Tupputi, in preparation.
[176] J.D., Vaaler, Some extremal problems in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183–216.Google Scholar
[177] G., Voronoï, Sur un problème du calcul des fonctions asymptotiques, J. Reine Angew. Math. 126 (1903), 241–282.Google Scholar
[178] G.N., Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, 1922.Google Scholar
[179] D.D., Wall, Normal numbers, Thesis, University of California, 1949.Google Scholar
[180] H., Weyl, Über ein problem aus dem gebiete der diophantischen approximationen, Nacr. Ges. Wiss. Gottingen (1914), 234–244.Google Scholar
[181] H., Weyl, Über die gleichverteilung von zhalen mod. eins, Math. Ann. 77 (1916), 313–352.Google Scholar
[182] R.L., Wheeden, A., Zygmund, Measure and integral. An introduction to real analysis, Pure and Applied Mathematics, 43, Marcel Dekker, 1977.Google Scholar
[183] Y., Zhang, Bounded gaps between primes, Ann. Math. 179 (2014), 1121–1174.Google Scholar
[184] G., Ziegler, The great prime number record races, Notices Amer. Math. Soc. 51 (2004), 414–416.Google Scholar
[185] A., Zygmund, Trigonometric series, I, II, Cambridge Mathematical Library, Cambridge University Press, 1993.Google Scholar

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  • References
  • Giancarlo Travaglini, Università degli Studi di Milano-Bicocca
  • Book: Number Theory, Fourier Analysis and Geometric Discrepancy
  • Online publication: 05 July 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107358379.013
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  • References
  • Giancarlo Travaglini, Università degli Studi di Milano-Bicocca
  • Book: Number Theory, Fourier Analysis and Geometric Discrepancy
  • Online publication: 05 July 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107358379.013
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Giancarlo Travaglini, Università degli Studi di Milano-Bicocca
  • Book: Number Theory, Fourier Analysis and Geometric Discrepancy
  • Online publication: 05 July 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107358379.013
Available formats
×