# The divisor problem for arithmetic progressions with small modulus

Acta Arithmetica (1992)

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

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topCharles E. Chace. "The divisor problem for arithmetic progressions with small modulus." Acta Arithmetica 61.1 (1992): 35-50. <http://eudml.org/doc/206450>.

@article{CharlesE1992,

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 = {http://eudml.org/doc/206450},

volume = {61},

year = {1992},

}

TY - JOUR

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 - http://eudml.org/doc/206450

ER -

## References

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- [FI2] J. B. Friedlander and H. Iwaniec, Incomplete Kloosterman sums and a divisor problem, Ann. of Math. 121 (1985), 319-350. Zbl0572.10029
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- [H3] D. R. Heath-Brown, The divisor function d₃(n) in arithmetic progressions, Acta Arith. 47 (1987), 29-56.
- [K] H. G. Kopetzky, Über die Größ enordnung der Teilerfunktion in Restklassen, Monatsh. Math. 82 (1976), 287-295. Zbl0347.10036
- [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
- [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.
- [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
- [Mn] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, 1971.
- [Mo] Y. Motohashi, An asymptotic series for an additive divisor problem, Math. Z. 170 (1980), 43-63. Zbl0411.10021
- [N] W. G. Nowak, On the divisor problem in arithmetic progressions, Comment. Math. Univ. St. Pauli 33 (1984), 209-217. Zbl0512.10035
- [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.
- [S] R. A. Smith, The generalized divisor problem over arithmetic progressions, Math. Ann. 260 (1982), 255-268. Zbl0467.10034
- [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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