Geodesic
The Average Number of Divisors in an Arithmetic Progression
Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 37-41

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

Let l and k be positive integers. Then for each integer n ≥ 1, define d(n; l, k) to be the number of (positive) divisors of n which lie in the arithmetic progression I mod k. Note that d(n;1,1) = d(n), the ordinary divisor function. 
Smith, R. A.; Subbarao, M. V. The Average Number of Divisors in an Arithmetic Progression. Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 37-41. doi: 10.4153/CMB-1981-005-3
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[1] 1. Berndt, B., On the average order of ideal functions and other arithmetic functions, Bull. Amer. Math. Soc. 76 (1962), 1270-1274. Google Scholar

[2] 2. Chandrasekharan, K. and Narasimhan, R., Functional equations with multiple gamma factors and the average order of arithmetic functions, Annals of Math. (2) 76 (1962), 93-136. Google Scholar

[3] 3. Lehmer, D. H., Euler's constant for arithmetic progressions, Acta Arith. 27 (1962), 125-142. Google Scholar

[4] 4. Prachar, K., Primzahlverteilung, Springer-Verlag, Berlin (1962). Google Scholar

[5] 5. Zogin, I. I., Certain asymptotic equations connected with the problem of Dirichlet on divisors. A generalization of the Dirichlet Theorem. Sverdlovsk. Gos. Ped. Inst. Ucen. Zap. 31 (1962), 87-96. Google Scholar

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