The divisor problem for arithmetic progressions with small modulus

Charles E. Chace

Acta Arithmetica (1992)

  • Volume: 61, Issue: 1, page 35-50
  • ISSN: 0065-1036

How to cite


Charles E. Chace. "The divisor problem for arithmetic progressions with small modulus." Acta Arithmetica 61.1 (1992): 35-50. <>.

author = {Charles E. Chace},
journal = {Acta Arithmetica},
keywords = {number of ordered -tuples; divisor problem; remainder},
language = {eng},
number = {1},
pages = {35-50},
title = {The divisor problem for arithmetic progressions with small modulus},
url = {},
volume = {61},
year = {1992},

AU - Charles E. Chace
TI - The divisor problem for arithmetic progressions with small modulus
JO - Acta Arithmetica
PY - 1992
VL - 61
IS - 1
SP - 35
EP - 50
LA - eng
KW - number of ordered -tuples; divisor problem; remainder
UR -
ER -


  1. [C] C. E. Chace, Writing integers as sums of products, doctoral dissertation, Colum- bia University, 1990. 
  2. [FI1] J. B. Friedlander and H. Iwaniec, The divisor problem for arithmetic progressions, Acta Arith. 45 (1985), 273-277. Zbl0572.10033
  3. [FI2] J. B. Friedlander and H. Iwaniec, Incomplete Kloosterman sums and a divisor problem, Ann. of Math. 121 (1985), 319-350. Zbl0572.10029
  4. [H1] D. R. Heath-Brown, Hybrid bounds for Dirichlet L-functions, Invent. Math. 47 (1978), 149-170. Zbl0362.10035
  5. [H2] D. R. Heath-Brown, The fourth power moment of the Riemann zeta function, Proc. London Math. Soc. (3) 38 (1979), 385-422. Zbl0403.10018
  6. [H3] D. R. Heath-Brown, The divisor function d₃(n) in arithmetic progressions, Acta Arith. 47 (1987), 29-56. 
  7. [K] H. G. Kopetzky, Über die Größ enordnung der Teilerfunktion in Restklassen, Monatsh. Math. 82 (1976), 287-295. Zbl0347.10036
  8. [L1] A. F. Lavrik, A functional equation for Dirichlet L-series and the problem of divisors in arithmetic progressions, Amer. Math. Soc. Transl. (2) 82 (1969), 47-65. Zbl0188.34801
  9. [L2] A. F. Lavrik, On the principal term in the divisor problem and the power series of the Riemann zeta-function in a neighborhood of its pole, English transl. in Proc. Steklov Inst. Math. 1979, no. 3, 175-183. 
  10. [Ma] K. Matsumoto, A remark on Smith's result on a divisor problem in arithmetic progressions, Nagoya Math. J. 98 (1985), 37-42. Zbl0545.10032
  11. [Mn] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, 1971. 
  12. [Mo] Y. Motohashi, An asymptotic series for an additive divisor problem, Math. Z. 170 (1980), 43-63. Zbl0411.10021
  13. [N] W. G. Nowak, On the divisor problem in arithmetic progressions, Comment. Math. Univ. St. Pauli 33 (1984), 209-217. Zbl0512.10035
  14. [P] M. M. Petečuk, The sum of values of the divisor function in arithmetic progressions whose difference is a power of an odd prime, Math. USSR-Izv. 15 (1980), 145-160. 
  15. [S] R. A. Smith, The generalized divisor problem over arithmetic progressions, Math. Ann. 260 (1982), 255-268. Zbl0467.10034
  16. [T] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed. revised by D. R. Heath-Brown, Clarendon Press, Oxford 1986. Zbl0601.10026

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