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The Average Number of Divisors in Certain Arithmetic Sequences

Mathematica Pannonica
Volume/Issue:
Volume 28_NS2: Issue 2
DOI:
https://doi.org/10.1556/314.2022.00019
Author:
Liubomir Chiriac

In this paper we study the sum ∑ p ≤ x   τ ( n p ) , where τ ( n ) denotes the number of divisors of n, and {np } is a sequence of integers indexed by primes. Under certain assumptions we show that the aforementioned sum is ≪   x  as  x   → ∞ . As an application, we consider the case where the sequence is given by the Fourier coefficients of a modular form.

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