ArticleOriginal scientific text
Title
The divisor problem for arithmetic progressions with small modulus
Authors 1
Affiliations
- Department of Mathematics, Williams College, Williamstown, Massachusetts 01267, U.S.A.
Bibliography
- [C] C. E. Chace, Writing integers as sums of products, doctoral dissertation, Colum- bia University, 1990.
- [FI1] J. B. Friedlander and H. Iwaniec, The divisor problem for arithmetic progressions, Acta Arith. 45 (1985), 273-277.
- [FI2] J. B. Friedlander and H. Iwaniec, Incomplete Kloosterman sums and a divisor problem, Ann. of Math. 121 (1985), 319-350.
- [H1] D. R. Heath-Brown, Hybrid bounds for Dirichlet L-functions, Invent. Math. 47 (1978), 149-170.
- [H2] D. R. Heath-Brown, The fourth power moment of the Riemann zeta function, Proc. London Math. Soc. (3) 38 (1979), 385-422.
- [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.
- [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.
- [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.
- [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.
- [N] W. G. Nowak, On the divisor problem in arithmetic progressions, Comment. Math. Univ. St. Pauli 33 (1984), 209-217.
- [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.
- [T] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed. revised by D. R. Heath-Brown, Clarendon Press, Oxford 1986.