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On the Digits of Sumsets

  • Christian Mauduit (a1), Joël Rivat (a2) and András Sárközy (a3)


Let $\mathcal{A}$ and $\mathcal{B}$ be large subsets of $\{1,\,.\,.\,.\,,\,N\}$ . We study the number of pairs $\left( a,b \right)\,\in \,\mathcal{A}\,\times \,\mathcal{B}$ such that the sum of binary digits of $a\,+\,b$ is fixed.



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[1] Alon, N. and Spencer, J. H., The probabilistic method. Third ed., Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, Inc., Hoboken, NJ, 2008.
[2] Balog, A., Rivat, J., and Sárközy, A., On arithmetic properties ofsumsets. Acta Math. Hungar. 144(2014), no. 1, 1842.http://dx.doi.Org/10.1007/s10474-014-0436-y
[3] Drmota, M., Subsequences of automatic sequences and uniform distribution. In: Uniform distribution and quasi-Monte Carlo methods, Radon Ser. Comput. Appl. Math., 15, De Gruyter, Berlin, 2014, pp. 87104.
[4] Drmota, M., Mauduit, C., and Rivat, J., The sum-of-digits function of polynomial sequences. J. Lond. Math. Soc. (2) 84(2011), no. 1, 81102.
[5] Drmota, M. and Morgenbesser, J. F., Generalized Thue-Morse sequences of squares. Israel J. Math. 190(2012), 157193.
[6] Fouvry, E. and Mauduit, C., Sur les entiers dont la somme des chiffres est moyenne. J. Number Theory 114(2005), no. 1, 135152. http://dx.doi.Org/10.1016/j.jnt.2005.03.007
[7] Gel'fond, A. O., Sur les nombres qui ont des propriétés additives et multiplicatives données. Acta Arith. 13(1967/1968), 259265.
[8] Martin, B., Mauduit, C., and Rivat, J., Théoréme des nombres premiers pour les fonctions digitales. Acta Arith. 165(2014), no. 1, 1145.
[9] Martin, B., Fonctions digitales le long des nombres premiers. Acta Arith. 170(2015), no. 2,175197.
[10] Mauduit, C., Propriétés arithmétiques des substitutions et automates infinis. Ann. Inst. Fourier 56(2006), no. 7, 25252549.http://dx.doi.Org/10.5802/aif.2248
[11] Mauduit, C. and Moreira, C. G., Phénoméne de Moser-Newman pour les nombres sans facteur carré. Bull. Soc. Math. France 143(2015), no. 3, 599617.
[12] Mauduit, C., Pomerance, C., and Sárközy, A., On the distribution in residue classes of integers with a fixed sum of digits. Ramanujan J. 9(2005), no. 1-2, 4562.http://dx.doi.Org/10.1007/s11139-005-0824-6
[13] Mauduit, C. and Rivat, J., Propriétés q-multiplicatives de la suite [nc╛, c > 1. Acta Arith. 118(2005), no. 2, 187203.
[14] Mauduit, C., La somme des chiffres des carrés. Acta Math. 203(2009), no. 1,107148.http://dx.doi.Org/10.1007/s11511-009-0040-0
[15] Mauduit, C., Sur un probléme de Gelfond: la somme des chiffres des nombres premiers. Ann. of Math. (2) 171(2010), no. 3, 15911646.http://dx.doi.Org/10.4007/annals.2010.1 71.1591
[16] Mauduit, C. and Sárközy, A., On the arithmetic structure of sets characterized by sum of digits properties. J. Number Theory 61(1996), no. 1, 2538.http://dx.doi.Org/10.1006/jnth.1996.0134
[17] Mauduit, C., On the arithmetic structure of the integers whose sum of digits is fixed. Acta Arith. 81(1997), no. 2, 145173.
[18] Newman, D. J. and Slater, M., Binary digit distribution over naturally defined sequences. Trans. Amer. Math. Soc. 213(1975), 7178.http://dx.doi.Org/10.1090/S0002-9947-1 975-0384734-3
[19] Spiegelhofer, L., Piatetski-Shapiro sequences via Beatty sequences. Acta Arith. 166(2014), no. 3, 201229.
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On the Digits of Sumsets

  • Christian Mauduit (a1), Joël Rivat (a2) and András Sárközy (a3)


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