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  1. Home
  2. Books
  3. Elliptic and Modular Functions from Gauss to Dedekind to Hecke
  • Cited by 9
Publisher:
Cambridge University Press
Online publication date:
April 2017
Print publication year:
2017
Online ISBN:
9781316671504
DOI:
https://doi.org/10.1017/9781316671504
Subjects:
Mathematics, History of Mathematics, Number Theory
Information

Book description

This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area.

Reviews

'Finally, it needs to be stressed that Roy does much more than present these mathematical works as museum pieces. He takes pains to tie them in to modern work when reasonable and appropriate, and that of course just adds to the quality of his work. I am very excited to have a copy of this wonderful book in my possession.'

Michael Berg Source: MAA Reviews

'This book will be a valuable resource for understanding modular functions in their historical context, especially for readers not fluent in the languages of the original papers.'

Paul M. Jenkins Source: Mathematical Reviews

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Contents

Contents
References
Bibliography
Abel, N. 1965. Oeuvres complètes, 2 vols. New York: Johnson Reprint.
Andrews, G. 1974. Applications of basic hypergeometric functions. SIAM Rev. 16, 441–484.
Andrews, G., and Berndt, B. 2005–. Ramanujan's Lost Notebook. New York: Springer.
Archibald, T. 2002. Charles Hermite and German Mathematics in France. In Parshall, K. H., and Rice, A. C., eds., Mathematics Unbound: The Evolution of an International Research Community,1800–1949, pp. 123–137. Providence, RI: AMS.
Armitage, J.V., and Eberlien, W. F. 2006. Elliptic Functions. Cambridge: Cambridge University Press.
Atkin, A. O. L. 1967. Proof of a Conjecture of Ramanujan. Glasgow Math J 8, 14–32.
Auwers, A. (ed). 1880. Briefwechsel zwischen Gauss und Bessel. Leipzig: Engelmann.
Bachmann, P. 1923. Die Arithmetik der quadratischen Formen. Leipzig: Teubner.
Barrow-Green, June. 1996. Poincaré and the Three Body Problem. Providence: AMS.
Bateman, P. T. 1951. On the representation of a number as the sum of three squares. Trans. Am. Math.Soc. 71, 70–101.
Berggren, L. J. M., Borwein, P. B., Borwein. 1997. Pi: A Source Book. New York: Springer-Verlag.
Berndt, B. 1985–1998. Ramanujan's Notebooks, parts I–V. New York: Springer-Verlag.
Berndt, B. 1992. Hans Rademacher (1892–1969). Acta Arith. 61, 209–231.
Berndt, B. 1993. Theta Functions: from the Classical to the Modern. Providence: AMS. edited by M. R., Murty. Chap. 1 Ramanujan's Theory of Theta-Functions, pages 1–63.
Berndt, B. 2005. Number Theory in the Spirit of Ramanujan. Providence: AMS.
Berndt, B., and Knopp, M. 2008. Hecke's Theory of Modular Forms and Dirichlet Series. Singapore: World Scientific.
Berndt, B., and Ono, K. 2001. The Andrews Festschrift. New York: Springer. edited by Foata, D., and Han, G.-N. Chap. Ramanujan's Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary, pages 39–110.
Berndt, B., and Rankin, R. 1995. Ramanujan: Letters and Commentary. Providence: AMS.
Berndt, B., and Rankin, R. 2001. Ramanujan: Essays and Surveys. Providence: AMS.
Bernoulli, Daniel. 1982–1996. Die Werke von Daniel Bernoulli. Basel: Birkhauser.
Bernoulli, Johann. 1968. Opera Omnia. Hildesheim: Georg Olms Verlag.
Bierman, K. R. (ed). 1977. Briefwechsel zwischen Alexander von Humboldt und Carl FriedrichGauss. Berlin: Akedemie-Verlag.
Birch, B. J. 1975. A look back at Ramanujan's notebooks. Math. Proc. Camb. Phil. Soc. 78, 73–79.
Boole, George. 1841. Exposition of a general theory of linear transformations, Parts I and II. Cambridge Math J 3, 1–20, 106–111.
Boole, George. 1844. Notes on linear transformations. Cambridge Math J. 4, 167–171.
Borwein, J. M., and Borwein, P. B. 1987. Pi and the AGM. New York: Wiley.
Bottazini, U., and Gray, J. 2013. Hidden Harmony-Geometric Fantasies. New York: Springer.
Brioschi, F. 1901. Opere Matematiche. Milano: Ulrico Hoepli.
Bruinier, Jan, Hendrik, and Ono, Ken. 2013. Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms. Advances in Math 246, 198–219.
Bruns, H. 1886. Über die Perioden der elliptischen Integrale erster und zweiter Gattung. Math. Annalen 27, no. 2, 234–252.
Cahen, E. 1891. Note sur un développement des quantités numériques, qui présente quelque analogie avec celui en fractions continues. Nouv. Ann. Math 10, 508–514.
Cahen, E. 1894. Sur la fonction ζ (s) de Riemann et sur des fonctions analogs. Ann. Sci. École Norm. Sup. 11, 75–164.
Cardano, G. 1993. ArsMagna or the Rules of Algebra. New York: Dover. translated by T. R.Wittmer.
Carr, G. S. 2013. A Synopsis of Elementary Results in Pure and Applied Mathematics. Cambridge: Cambridge University Press.
Cassels, J. W. S. 1973. Louis Joel Mordell. Biog. Mem. Fellows Royal Soc. 19, 493–520.
Cauchy, A. L. 1882–1974. Oeuvres complètes. Paris: Gauthier-Villars.
Cayley, A. 1874. A memoir on the transformation of elliptic functions. Phil. Trans. Royal Soc. 164, 397–456.
Cayley, A. 1889–1898. Collected Mathematical Papers. Cambridge: Cambridge University Press.
Chan, H. H., and Chua, K. S. 2003. Papers in Memory of Robert A. Rankin. Norwell, MA: Kluwer Acad. Press. Chap. Representations of Integers as Sums of 32 Squares, pages 79–89.
Chowla, S. D. 1934. Congruence properties of partitions. JLMS 9, 247.
Clairaut, A. C. 1739. Recherches générales sur le calcul intégral. Mém. de l'Académie Royale des Sci. 1, 425–436.
Clairaut, A. C. 1740. Sur l'intégration ou la construction des équations différentielles du premier ordre. Mém. de l'Académie Royale des Sci. 2, 293–323.
Clarke, F. M. 1929. Thomas Simpson and his Times. Baltimore: Waverly Press.
Cooper, S. 2001. On sums of an even number of squares, and an even number of triangular numbers: an elementary approach based on Ramanujan's 1ψ1 summation formula. ContemporaryMath, 291, 115–138.
Cotes, Roger. 1722. Harmonia Mensurarum. Cambridge: Cambridge University Press.
de Moivre, Abraham. 1707. Aequationum quarundam Potestatis tertiae, quintae, septimae, novae, & superiorum, ad infinitum usque pergendo, in terminis finitis, ad imstar Regularum pro Cubicis quae vocantur, Cardani, Resolutio Analytica. Phil. Trans. 25, no. 309, 2368–2371.
de Moivre, Abraham. 1730. Miscellanea analytica de seriebus et quadraturis. London: Touson and Watts.
de Moivre, Abraham. 1967. The Doctrine of Chances. New York: Chelsea.
Dedekind, R. 1930–. Gesammelte MathematischeWerke. Braunschweig: Vieweg. edited by R., Fricke, E., Noether, Ø. Ore.
Deligne, P. 1974. La conjecture de Weil. I. Pub. Math IHES 43, 273–307.
Dewar, Michael, and Murty, M. Ram. 2013. A derivation of the Hardy-Ramanujan formula from an arithmetic formula. Proc. AMS 141, 1903–1911.
Dirichlet, L., and Dedekind, R. 1999. Lectures on Number Theory. Providence: AMS. translated by John, Stillwell.
Dirichlet, P. G. L. 1969. Mathematische Werke. New York: Chelsea.
Dunnington, G. 2004. Gauss: Titan of Science. Washington: MAA.
Edwards, H. M. 1984. Galois Theory. New York: Springer-Verlag.
Eisenstein, G. 1847. Mathematische Abhandlungen, besonders aus dem Gebiete der höheren Arithmetik und der Elliptischen Funktionen. Berlin: G. Riemer.
Eisenstein, G. 1975. Mathematische Werke. New York: Chelsea.
Elfving, G. 1981. The History of Mathematics in Finland, 1828–1918. Helsinki: Societas Scientiarum Fennica.
Elstrodt, J. 2007. Analytic Number Theory: A tribute to Gauss and Dirichlet. Providence: AMS. edited by Duke, W. and Tschinkel, Y. Chap. The life and work of Gustav Lejeune Dirichlet (1905–1859), pages 1–37.
Engelsman, S. B. 1984. Families of Curves and the Origins of Partial Differentiation. Amsterdam: North Holland.
Enneper, A. 1890. Elliptische Functionen. Halle: Louis Nebert.
Euler, L. 1911–. Leonhardi Euleri Opera Omnia. Series I-IV A. Bassel: Birkhäuser.
Euler, Leonhard. 1988. Introduction to Analysis of the Infinite. New York: Springer-Verlag. translated by J. D., Blanton.
Fagnano, G. C. 1750. Produzioni Matematiche del Conte Giulio Carlo di Fagnano. Pesaro: Gavelli.
Feigenbaum, L. 1981. Brook Taylor's Methodus Incrementorum: A Translation with Mathematicaland Historical Commentary. Ph.D. thesis, Yale University, New Haven.
Fine, N. J. 1988. Basic Hypergeometric Series and Applications. Providence: AMS.
Ford, L. R. 1957. Automorphic Functions. New York: Chelsea.
Fuss, P. H. (ed). 1968. Correspondance mathématique et physique, 3 vols. New York: Johnson Reprint.
Gårding, L. 1997. Mathematics and Mathematicians: Mathematics in Sweden before 1950. Providence: AMS.
Gårding, L., and Skau, C. 1994. Niels Henrik Abel and solvable equations. Arch. Hist. of Exact Sc. 48, 81–103.
Gannon, T. 2006. Moonshine Beyond the Monster. Cambridge: Cambridge University Press.
Gauss, C. F. 1863–1927. Werke, vols. 1–12. Leipzig: Teubner.
Gauss, C. F. 1965. Disquisitiones Arithmeticae, English trans. Arthur, A. Clarke, S. J. New Haven: Yale.
Gelfand, Kapranov, Zelevinsky. 1994. Discriminants, Resultants, and Multidimensional Determinants. Boston: Birkhäuser.
Glaisher, J.W. L. 1907a. On the number of representations of a number as a sum of 2r squares, where 2r does not exceed eighteen. Proc. London Math. Soc. series 2, 5, 479–490.
Glaisher, J. W. L. 1907b. On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares. Quarterly J. Pure and Appl. Math. 38, 1–62.
Glaisher, J. W. L. 1908. On elliptic-function expansions in which the coefficients are powers of the complex numbers having n as norm. Quart. J. Pure and Appl. Math 39, 266–300.
Goldstein, Schappacher, Schwermer (ed). 2007. The Shaping of Arithmetic after C. F. Gauss's Disquisitiones Arithmeticae. New York: Springer.
Gowing, R. 1983. Roger Cotes. Cambridge: Cambridge University Press.
Gray, J. 1986. Linear Differential Equations and Group Theory from Riemann to Poincaré. Boston: Birkhäuser.
Green, George. 1970. Mathematical Papers. New York: Chelsea.
Grosswald, E. 1985. Representations of Integers as Sums of Squares. New York: Springer-Verlag.
Gudermann, C. 1838. Theorie der Modular-Functionen und der Modular-Integrale. J. Reine undAngew. Math. 18, 1–54, 220–258.
Guetzlaff, C. 1834. Aequatio modularis pro transformatione functionum ellipticarum septimi ordinis.J. Reine Angew. Math. 12, 173–177.
Gupta, H. 1935. Tables of partitions. PLMS, series 2 39, 142–149.
Hardy, G. H. 1966–1979. Collected Papers of G. H. Hardy. Oxford: Oxford University Press.
Hardy, G. H. 1978. Ramanujan. New York: Chelsea.
Hardy, G. H., and Riesz, M. 1915. The General Theory of Dirichlet Series. Cambridge: Cambridge University Press.
Hecke, E. 1959. Mathematische Werke. Göttingen: Vandenhoeck und Ruprecht.
Hecke, E. 1983. Lectures on Dirichlet Series, Modular Functions and Quadratic Forms. Göttingen:Vandenhoeck and Ruprecht.
Hermite, C. 1905–1917. Oeuvres. Paris: Gauthier-Villars.
Hille, E. 1997. Ordinary Differential Equations in the Complex Domain. New York: Dover.
Hurwitz, A. 1962. Mathematische Werke. Basel: Birkhäuser.
Jacobi, C. G. J. 1846. Opuscula Mathematica, vol. 1. Berlin: G. Reimer.
Jacobi, C. G. J. 1965. Mathematische Werke. New York: Chelsea.
Joubert, C. 1858. Sur divers équations analogues aux équations modulaires dans la théorie des fonctions elliptiques. Comptes Rendus 47, 337–345.
Joubert, C. 1875. Sur les équations qui se recontrent dans la théorie de la transformation des fonctions elliptiques. Paris: Gauthier-Villars.
Kiepert, L. 1879a. Auflösung der Gleichungen fünften Grades. J. Reine Angew. Math. 87, 114–133.
Kiepert, L. 1879b. Zur Transformationstheorie der elliptischen Functionen. J. Reine Angew. Math. 87, 199–216.
Klein, F. 1921–1923. Gessamelte Mathematische Abhandlungen . Berlin: Verlag Julius Springer.
Klein, F. 1933. Vorlesungen über die hypergeometrische Funktion. Berlin: Springer. Compiled and edited by Otto Haupt.
Klein, F. 1956. The Icosahedron. New York: Dover. translated by George, Morrice.
Klein, F., and Fricke, R. 1890–1892. Vorlesungen über die Theorie der Modulfunktionen Leipzig: Teubner.
Knopp, M. 2000. Number Theory. New Delhi: Hindustan Book Agency. edited by Bambah, R. P., et al., Chap. Hamburger's theorem on ζ (s) and the abundance principle for Dirichlet series with fundamental equations, pages 201–216.
Knuth, Donald. 1998. The Art of Computer Programming (third edition), vol. 2. Reading, MA: Addison-Wesley.
Kronecker, L. 1968. Mathematische Werke. New York: Chelsea.
Kronecker, Leopold. 1894. Theorie der einfachen und der vielfachen Integrale. Leipzig: Teubner. edited by E., Netto.
Kuhn, H. K. 1991. History of Mathematical Programming: a collection of personal reminiscences. Amsterdam: North-Holland. edited by Lenstra, Kan, and Schrijver. Chap. Nonlinear programming: A historical note, pages 82–96.
Kummer, Ernst. 1975. Collected Papers. Berlin: Springer Verlag.
Lacroix, S. F. 1819. Traité du calcul différential et du calcul intégral, Vol. 3. Paris: Courcier.
Lagrange, J. L. 1867–1892. Oeuvres, vols. 1–14. Paris: Gauthier-Villars.
Landau, E. 1906. Euler und die Funktionalgleichung der Riemannschen Zetafunktion. Bibliotheca Math. 7, no. 3, 69–79.
Landen, J. 1775. An investigation of a general theorem for finding the length of any arc of any conic hyperbola, by means of two elliptic arcs, with some other new and useful theorems deduced therefrom. Phil. Trans. Roy. Soc. Lon. 65, 283–289.
Legendre, A. M. 1792. Mémoire sur les Transcendantes elliptiques. Paris: Academie des Sciences.
Legendre, A. M. 1811–1817. Exercices de calcul intégral, 2 vols. Paris: Courcier.
Lehmer, D. H. 1937. On the Hardy-Ramanujan series for the partition function. J. London Math. Soc. 12, 171–176.
Leibniz, G. W. 1920. The Early Mathematical Manuscripts of Leibniz. Chicago: Open Court. edited by Gerhardt, C. I., translated with notes by Child, J. M.
Leibniz, G.W. 1971. Mathematische Schriften. Hildesheim: Georg Olms Verlag. edited by Gerhardt, C. I.
Leybourn, Thomas. 1817. The mathematical questions, proposed in the Ladies'diary, and their original answers, together with some new solutions, from its commencement in the year 1704 to 1816. London: Mawman.
Lindelöf, E. 1905. Le calcul des résidus et ses applications à la théorie des fonctions. Paris: Gauthier- Villars.
Liouville, J. 1844. Nouvelle démonstration d'un théorème sur les irrationnelles algébriques. Comptes Rendus, 18, 910–911.
Liouville, J. 1880. Leçons sur les fonctions doublement périodiques. J. Reine Angew. Math. 88, 277– 310.
Lützen, J. 1990. Joseph Liouville 1809–1882. New York: Springer-Verlag.
Markushevich, A. 1992. Introduction to the classical theory of Abelian functions. Providence: AMS.
McKean, H., and Moll, V. 1997. Ellipitc Curves. Cambridge: Cambridge University Press.
Milne, S. C. 2002. Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions,Continued Fractions, and Schur Functions. Boston: Kluwer Acad. Press.
Minkowski, H. 1967. Gesammelte Abhandlungen. Leipzig: Teubner.
Mittag-Leffler, G. 1923. An introduction to the theory of elliptic functions. Ann. Math. 24, 271– 351.
Mordell, L. 1917a. On Mr. Ramanujan's empirical expansions of modular functions. Proc. Camb. Phil. Soc. 19, 117–124.
Mordell, L. 1917b. On the representation of numbers as a sum of 2r squares. Quart. J. Pure and Appl. Math 48, 93–104.
Mordell, L. 1919. On the representation of numbers as a sum of an odd number of squares. Trans. Camb. Phil. Soc. 22, 361–372.
Mordell, L. 1923. On the integer solutions of the equation ey2 = ax3 + bx2 + cx + d. Proc. London Math. Soc. 21, 415–419.
Mordell, L. 1929. Poisson's summation formula in several variables and some applications in the theory of numbers. Proc. Camb. Phil. Soc. 25, 412-420.
Moreno, C. J., and Wagstaff, Jr, S. S. 2006. Sums of Squares of Integers. Boca Raton: Chapman and Hall.
Müller, F. 1867. De transformatione functionum ellipticarum. Berlin: A. W. Schade.
Murty, M. R., and Murty, V. K. 2013. The Mathematical Legacy of Srinivasa Ramanujan. New Delhi: Springer.
Neumann, P. M. 2011. The Mathematical Writings of Évariste Galois. Zürich: European Mathematical Society Publishing House.
Newman, J. 1956. The World of Mathematics, 4 vols. New York: Simon and Schuster.
Newton, Isaac. 1959–1960. The Correspondence of Isaac Newton. Cambridge: Cambridge University Press. edited by Turnbull, H. W.
Newton, Isaac. 1967–1981. The Mathematical Papers of Isaac Newton. Cambridge: Cambridge University Press. edited by Whiteside, D. T.
Ono, K. 2002. Representations of integers as sums of squares. J. Number Theory 95, 253–258.
Ono, K., and Aczel, A. 2016. My Search for Ramanujan. Cham: Springer.
Peiffer, J. 1983. Joseph Liouville (1809–1882): ses contributions à la théorie des fonctions d'une variable complexe. Rev. Hist. Sci. 36, 209–248.
Peters, C. A. F. (ed). 1860–1865. Briefwechsel zwischen C. F. Gauss und H. C. Schumacher, vols. 1–6. Altona: Gustav Esch.
Pieper, H. (ed). 1987. Briefwechsel zwischen Alexander von Humboldt und C. G. Jacob Jacobi. Berlin: Akademie-Verlag.
Rademacher, H., and Grosswald, E. 1972. Dedekind Sums. Washington: MAA.
Rademacher, Hans. 1974. Collected Papers. Cambridge, MA: MIT Press.
Ramanujan, S. 1988. The lost notebook and other unpublished papers. New Delhi: Narosa.
Ramanujan, S. 2000. Collected Papers. Providence: AMS Chelsea.
Rangachari, S. S. 1982. Ramanujan and Dirichlet series with Euler products. Proc. Indian Acad. Soc. (Math Sci.) 91, 1–15.
Rankin, R. 1946. A certain class of multiplicative functions. Duke Math. J. 13, 281–306.
Rankin, R. 1962. On the representation of a number as the sum of any number of squares, and in particular of twenty. Acta Arithmetica 7, 399–407.
Rankin, R. 1965. Sums of squares and cusp forms. Amer. J. Math. 87, 857–862.
Rankin, R. 1977. Modular Forms and Functions. Cambridge: Cambridge University Press.
Remmert, R. 1991. Theory of Complex Functions, An English translation of the second edition of Remmert's Functionentheorie I. New York: Springer-Verlag. translated by Robert B., Burckel.
Riemann, B. 1899. Elliptische functionen. Vorlesungen von Bernhard Riemann. Mit zusätzen herausgegeben von Hermann Stahl. Leipzig: Teubner.
Riemann, B. 1990. Gessammelte Mathematische Werke. Berlin: Springer-Verlag.
Rigaud, S. P. (ed). 1841. Correspondence of Scientific Men of the Seventeenth Century. Oxford: Oxford University Press.
Rochat, Vecten, Fauquier, and Pilatte. 1811–12. Questions résolves. Solutions des deux problèmes proposés à la page 384 du premier volume des Annales. Annales de Math. Pure et Appl. II, 88–93.
Rodríguez, I. Kra, Gilman. 2012. Complex Analysis in the Spirit of Lipman Bers. 2nd ed. New York: Springer.
Ronan, M. 2006. Symmetry and the Monster. New York: Oxford University Press.
Roy, R. 2011. Sources in the Development of Mathematics. Cambridge, New York: Cambridge University Press.
Russ, S. B. 1980. A translation of Bolzano's paper on the intermediate value theorem. Hist. Math. 7, 156–185.
Scharlau, W. 1981. Richard Dedekind 1831–1981: Eine Würdigung zu seinem 150. Geburtstag. Braunschweig/Wiesbaden: Vieweg und Teubner.
Scheibner, W. 1860. Über unendliche Reihen und deren Convergenz. Leipzig: S. Hirzel.
Schwarz, H. A. 1972. Gesammelte Mathematische Abhandlungen. New York: Chelsea.
Serre, J. P. 1966. Seminar on Complex Multiplication. Berlin: Springer. edited by Borel, A. et al., Chap. II Modular forms, pages 1–16.
Shen, L. C. 1993. On the logarithmic derivative of a theta function and a fundamental identity of Ramanujan. J. Math. Anal. Appl. 177, no. 1, 299–307.
Shimura, G. 2002. The representation of integers as sums of squares. Amer. J. Math, 124, 1059–1081.
Simpson, Thomas. 1759. The invention of a general method for determining the sum of every second, third, fourth, or fifth, etc. term of a series, taken in order; the sum of the whole being known. Phil.Trans. 50, 757–769.
Smith, D. E. 1959. A Source Book in Mathematics. New York: Dover.
Smith, H. J. S. 1865. Report on the Theory of Numbers. N.p.: Brit. Assoc. for the Advancement of Science.
Smith, H. J. S. 1965. Collected Mathematical Papers. New York: Chelsea.
Smithies, F. 1997. Cauchy and the Creation of Complex Function Theory. Cambridge: Cambridge University Press.
Sohnke, L. 1837. Aequationes modulares pro transformatione Functionum Ellipticarum. J. ReineAngew. Math 16, 97–130.
Stäkel, P., and Ahrens, W. (eds). 1908. Der Briefwechsel zwischen C. G. J. Jacobi und P. H. Fuss überdie Herausgabe der Werke Leonhard Eulers. Leipzig: Teubner.
Stalker, J. 1998. Complex Analysis: The fundamentals of the classical theory of functions. Boston: Birkhäuser.
Stirling, James, and Tweddle, Ian. 2003. James Stirling's Methodus Differentialis An Annotated Translation of Stirling's Text. London: Springer.
Sylvester, J. J. 1973. Mathematical Papers. New York: Chelsea.
Tannery, J., and Molk, J. 1972. Éléments de la théorie des fonctions elliptiques, 4 vols. New York: Chelsea.
Taylor, B. 1715. Methodus Incrementorum. London: Gulielmi Innys. Translation into English in Feigenbaum (1981).
Titchmarsh, E. C., and Heath-Brown. 1986. The Theory of the Riemann Zeta-function, second edition. New York: Oxford University Press.
Uspensky, J. 1928. On Jacobi's arithmetical theorems concerning the simultaneous representation of numbers by two different quadratic forms. Trans. Am. Math. Soc. 30, 385–404.
van der Waerden, B. L. 1975. On the sources of my book, Modern Algebra. Hist. Math. 2, 32–40.
Waring, Edward. 1988. Meditationes Algebraicae. Providence: AMS. translated by Dennis, Weeks.
Weber, H. 1894–1908. Lehrbuch der Algebra. Braunschweig: Vieweg.
Weierstrass, K. 1894–1927. Mathematische Werke. Berlin: Mayer und Müller.
Weil, A. 1976. Elliptic Functions according to Eisenstein and Kronecker. Berlin: Springer-Verlag.
Weil, A. 1980. Oeuvres Scientifiques. New York: Springer-Verlag.
Weil, A. 1984. Number Theory: An approach through history from Hammurapi to Legendre. Boston: Birkhäuser.
Williams, K. 2011. Number Theory in the Spirit of Liouville. Cambridge: Cambridge University Press.
Zagier, D. 2000. A proof of the Kac-Wakimoto affine denominator formula for the strange series. Math. Res. Letters 7, 597–604.

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