Soit , . Pour , on note la somme des chiffres de en base . Nous donnons des majorations de sommes d’exponentielles de la forme
Let , . For , denote by the sum of digits of in the -ary digital expansion. We give upper bounds for exponential sums like
Classification : 11L07, 11B85, 11A63
Mots clés : sommes des chiffres, répartition dans les progressions arithmétiques, fonctions multiplicatives
@article{AIF_2005__55_7_2423_0, author = {Dartyge, C\'ecile and Tenenbaum, G\'erald}, title = {Sommes des chiffres de multiples d'entiers}, journal = {Annales de l'Institut Fourier}, pages = {2423--2474}, publisher = {Association des Annales de l'institut Fourier}, volume = {55}, number = {7}, year = {2005}, doi = {10.5802/aif.2166}, zbl = {05015294}, mrnumber = {2207389}, language = {fr}, url = {www.numdam.org/item/AIF_2005__55_7_2423_0/} }
Dartyge, Cécile; Tenenbaum, Gérald. Sommes des chiffres de multiples d'entiers. Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2423-2474. doi : 10.5802/aif.2166. http://www.numdam.org/item/AIF_2005__55_7_2423_0/
[4] Sur la représentation des multiples d'un entier dans une base (Publications mathématiques d'Orsay, 83.04, Colloque Hubert Delange (7-8 juin 1982), 20-37) | MR 728398 | Zbl 0521.10045
[6] Congruences de sommes de chiffres de valeurs polynomiales (Bull. London Math. Soc., à paraître) | Zbl 05014334
[9] Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta arith., Volume 13 (1968), pp. 259-265 | MR 220693 | Zbl 0155.09003
[15] On the number of binary digits in a multiple of three, Proc. Amer. Math. Soc., Volume 21 (1969), pp. 719-721 | Article | MR 244149 | Zbl 0194.35004
[16] Binary digit distribution over naturally defined sequences, Trans. Amer. Math. Soc., Volume 213 (1975), pp. 71-78 | Article | MR 384734 | Zbl 0324.10053
[3] The asymptotic sieve, Rend. Accad. Naz., Volume XL (5) 1/2 (1975/76), pp. 243-269 ((1977)) | MR 491570 | Zbl 0422.10042
[13] Rosser's sieve, Acta arith., Volume 36 (1980), pp. 171-202 | MR 581917 | Zbl 0435.10029
[22] Integers whose multiples have anomalous digital frequencies, Acta arith., Volume 38 (1980), pp. 117-128 | MR 604228 | Zbl 0448.10010
[18] The joint distribution of the digits of certain integer -tuples, Studies in Pure Mathematics in Memory of P. Turán, Birkhäuser (1983), pp. 605-622 | MR 820255 | Zbl 0523.10030
[17] The joint distribution of the binary digits of integer multiples, Acta arith., Volume 63 (1984), pp. 391-415 | MR 756290 | Zbl 0489.10008
[20] A theorem of metric diophantine approximation and estimates for sums involving binary digits (1985) (Thèse)
[5] On a convolution method (1989), pp. 110-137 | MR 1203323
[19] On elementary methods in prime-number theory and their limitations, Collected Works vol. I (1989), pp. 388-397 | Zbl 0048.03101
[21] On the joint distribution of digital sums, Journal number theory, Volume 33 (1989), pp. 132-151 | Article | MR 1034195 | Zbl 0678.10037
[1] Unimodalité de la distribution du nombre de diviseurs premiers d'un entier, Ann. Inst. Fourier, Grenoble, Volume 40 (1990) no. 2, pp. 255-270 | Article | Numdam | MR 1070828 | Zbl 0711.11030
[23] Sur une question d'Erdos et Schinzel, A Tribute to Paul Erdos, Cambridge University Press, 1990, pp. 405-443 | MR 1117034 | Zbl 0713.11069
[24] Introduction à la théorie analytique et probabiliste des nombres, 2 édition, Cours spécialisés, Société mathématique de France, 1995 no. 1 | MR 1366197 | Zbl 0880.11001
[7] Sommes des chiffres et nombres presque premiers, Math. Ann., Volume 305 (1996), pp. 571-599 | Article | MR 1397437 | Zbl 0858.11050
[10] Sets of multiples, Cambridge Tracts in Mathematics, Volume 118 (1996) (Cambridge University Press, Cambridge) | MR 1414678 | Zbl 0871.11001
[26] Exercices corrigés de théorie analytique et probabiliste des nombres, Cours spécialisés, Société mathématique de France, 1996 no. 2 | MR 1397501 | Zbl 0873.11002
[2] On an additive property of stable sets (London Math. Soc. Lecture Note Ser.) Volume 237, Cambridge Univ. Press, Cambridge, 1997, pp. 55-63 ((Cardiff, 1995)) | MR 1635722 | Zbl 0924.11011
[14] On finite pseudorandom binary sequences, II. The Champernowne, Rudin-Shapiro, and Thue-Morse sequences : a further construction, Journal number theory, Volume 72 (1998), pp. 1-21 | MR 1657960 | Zbl 0916.11047
[25] A rate estimate in Billingsley's theorem for the size distribution of large prime factors, Quart. J. Math., Volume 51 (2000), pp. 385-403 | Article | MR 1782101 | Zbl 1004.11050
[11] Investigations in the theory of -additive and -multiplicative functions, I, Acta Math. Hungar., Volume 91 (2001) no. (1-2), pp. 53-78 | Article | MR 1912360 | Zbl 0980.11001
[12] Investigations in the theory of -additive and -multiplicative functions, II, Acta Math. Hungar., Volume 97 (2002) no. (1-2), pp. 97-108 | Article | MR 1932796 | Zbl 1012.11008
[F8] Méthodes de crible et fonctions sommes des chiffres, Acta Arith., Volume 77 (1996) no. 4, pp. 339-351 | MR 1414514 | Zbl 0869.11073