On the arithmetic structure of the integers whose sum of digits is fixed

Christian Mauduit; András Sárközy

Acta Arithmetica (1997)

  • Volume: 81, Issue: 2, page 145-173
  • ISSN: 0065-1036

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Christian Mauduit, and András Sárközy. "On the arithmetic structure of the integers whose sum of digits is fixed." Acta Arithmetica 81.2 (1997): 145-173. <http://eudml.org/doc/207059>.

@article{ChristianMauduit1997,
author = {Christian Mauduit, András Sárközy},
journal = {Acta Arithmetica},
keywords = {sum of digits function; -additive function; fixed sum of digits; well-distributed; residue classes; application of the large sieve},
language = {eng},
number = {2},
pages = {145-173},
title = {On the arithmetic structure of the integers whose sum of digits is fixed},
url = {http://eudml.org/doc/207059},
volume = {81},
year = {1997},
}

TY - JOUR
AU - Christian Mauduit
AU - András Sárközy
TI - On the arithmetic structure of the integers whose sum of digits is fixed
JO - Acta Arithmetica
PY - 1997
VL - 81
IS - 2
SP - 145
EP - 173
LA - eng
KW - sum of digits function; -additive function; fixed sum of digits; well-distributed; residue classes; application of the large sieve
UR - http://eudml.org/doc/207059
ER -

References

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  1. [Ell] P. D. T. A. Elliott, Probabilistic Number Theory, I, Mean-Value Theorems, Grundlehren Math. Wiss. 239, Springer, 1979. 
  2. [Ell-S] P. D. T. A. Elliott and A. Sárközy, The distribution of the number of prime divisors of sums a+b, J. Number Theory 29 (1988), 94-99. Zbl0646.10042
  3. [Er-P-S-S] P. Erdős, C. Pomerance, A. Sárközy and C. L. Stewart, On elements of sumsets with many prime factors, ibid. 44 (1993), 93-104. Zbl0780.11040
  4. [Ess] C. G. Esseen, Fourier analysis of distribution functions. A mathematical study of Laplace-Gaussian law, Acta Math. 77 (1945), 1-125. Zbl0060.28705
  5. [Fin] M. N. J. Fine, The distribution of the sum of digits (mod p), Bull. Amer. Math. Soc. 71 (1965), 2651-2652. 
  6. [F-M1] E. Fouvry et C. Mauduit, Somme des chiffres et nombres presque premiers, Math. Ann. 305 (1996), 571-599. 
  7. [F-M2] E. Fouvry et C. Mauduit, Crible asymptotique de Bombieri et somme des chiffres, preprint. 
  8. [Gel] A. O. Gelfond, Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta Arith. 13 (1968), 259-265. Zbl0155.09003
  9. [Mau] C. Mauduit, Substitutions et ensembles normaux, Habilitation Dir. Rech., Université Aix-Marseille II, 1989. 
  10. [M-S] C. Mauduit and A. Sárközy, On the arithmetic structure of sets characterized by sum of digits properties, J. Number Theory 61 (1996), 25-38. Zbl0868.11004
  11. [Mon] H. L. Montgomery, The analytic principle of the large sieve, Bull. Amer. Math. Soc. 84 (1978), 547-567. Zbl0408.10033
  12. [P-S] G. Pólya and G. Szegő, Problems and Theorems in Analysis, II, Grundlehren Math. Wiss. 216, Springer, 1976. 
  13. [S-S] A. Sárközy and C. L. Stewart, On divisors of sums of integers, V, Pacific J. Math. 166 (1994), 373-384. Zbl0841.11049
  14. [Ten] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publ. Inst. Elie Cartan, 13, 1990. 

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