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arXiv · 2607.27131

On the second moment and non-vanishing of central values of Hecke $L$-functions of $r$-th order characters

Adrian Diaconu·Bogdan Ion·Vicenţiu Paşol·Alexandru A. Popa
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Abstract

In this paper, we establish asymptotic formulas for the first and second twisted moments of $r$-th order Hecke $L$-functions over global fields that contain the $2r$-th roots of unity, for $r\ge 3$. We focus primarily on algebraic number fields. As a consequence, we establish a positive proportion of non-vanishing central values for these $L$-functions, specifically for families of both square-free and $r$-th power-free ideals. Our approach is based on the machinery of multiple Dirichlet series.

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Adrian Diaconu, Bogdan Ion, Vicenţiu Paşol, Alexandru A. Popa. 2026-07-29. On the second moment and non-vanishing of central values of Hecke $L$-functions of $r$-th order characters. https://arxiv.org/abs/2607.27131

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