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arXiv · 2309.08057

Mean values of long Dirichlet polynomials with divisor coefficients

Fatma Cicek·Alia Hamieh·Nathan Ng
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Abstract

In this article, we prove an asymptotic formula for the mean value of long smoothed Dirichlet polynomials with divisor coefficients. Our result has a main term that includes all lower order terms and a power saving error term. This is derived from a more general theorem on mean values of long smoothed Dirichlet polynomials that was previously established by the second and third authors. We thus establish a stronger form of a conjecture of Conrey and Gonek in the case of divisor functions.

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Fatma Cicek, Alia Hamieh, Nathan Ng. 2023-09-14. Mean values of long Dirichlet polynomials with divisor coefficients. https://doi.org/10.2140/ant.2025.19.1427

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