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arXiv · 1610.06900

The variance of divisor sums in arithmetic progressions

Brad Rodgers·Kannan Soundararajan
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Abstract

We study the variance of sums of the $k$-fold divisor function $d_k(n)$ over sparse arithmetic progressions, with averaging over both residue classes and moduli. In a restricted range, we confirm an averaged version of a recent conjecture about the asymptotics of this variance. This result is closely related to moments of Dirichlet $L$-functions and our proof relies on the asymptotic large sieve.

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Brad Rodgers, Kannan Soundararajan. 2016-10-21. The variance of divisor sums in arithmetic progressions. https://doi.org/10.1515/forum-2016-0227

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