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arXiv · 2410.16940

A segment of Euler product associated to a certain Dirichlet series

Rajat Gupta·Aditi Savalia
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Abstract

In the spirit of the work of Hardy-Littlewood and Lavrik, we study the Dirichlet series associated to the generalized divisor function $\sigma_{\alpha}(n):=\sum_{d|n}d^{\alpha}$. We obtain an exact identity relating the Dirichlet series $\zeta(s)\zeta(s-\alpha)$ and a segment of the Euler product attached to it. Specifically, our main theorems are valid in the critical strip.

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Rajat Gupta, Aditi Savalia. 2024-10-22. A segment of Euler product associated to a certain Dirichlet series. https://doi.org/10.1016/j.jnt.2024.06.003

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