Geodesic
Divisors of Integers in Arithmetic Progression
Canadian mathematical bulletin, Tome 33 (1990) no. 2, pp. 129-134

Voir la notice de l'article provenant de la source Cambridge University Press

Let d(n; l, k) be the number of positive divisors of n which lie in the arithmetic progression l mod k. Using the complex integration technique the formula is proved. This formula holds uniformly in l, k and x satisfying 1 ≦ l ≦ k, (lx)1/2 ≦ k ≦ x1-∊ ; the exponent α ≦ 1/3.
DOI : 10.4153/CMB-1990-022-8
Mots-clés : 11N37, 11M35, 11M41 
Varbanec, P. D.; Zarzycki, P. Divisors of Integers in Arithmetic Progression. Canadian mathematical bulletin, Tome 33 (1990) no. 2, pp. 129-134. doi: 10.4153/CMB-1990-022-8
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[1] 1. Smith, R. A., Subbarao, M. V., The average number of divisors in an arithmetic progression, Canad. Math. Bull. 24 (1981), 37–41. Google Scholar

[2] 2. Nowak, W. G., On a result of Smith and Subbarao concerning a divisor problem, Canad. Math. Bull. 27 (1984), 501–504. Google Scholar

[3] 3. Fedoruk, M. V., Saddle-point method, Moscow (1977) (in Russian). Google Scholar

[4] 4. Titchmarsh, E. C., The theory of the Riemann zeta-function, Oxford (1951). Google Scholar

[5] 5. Kolesnik, G. A., On the estimation of some exponential sums, Acta Arith., XXV (1973), 7–30. Google Scholar

[6] 6. Kolesnik, G. A., On the order o/C((l/2) + it) and A(R), Pacific J. Math. 98 (1982), 107–122. Google Scholar

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