Mollified Moments of Cubic Dirichlet L-Functions over the Eisenstein Field

Ahmet M. Güloğlu; Hamza Yesilyurt

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arXiv · 2301.10979

Mollified Moments of Cubic Dirichlet L-Functions over the Eisenstein Field

Ahmet M. Güloğlu·Hamza Yesilyurt

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Abstract

We prove, assuming the generalized Riemann Hypothesis (GRH) that there is a positive density of $L$-functions associated with primitive cubic Dirichlet characters over the Eisenstein field that do not vanish at the central point $s=1/2$. This is achieved by computing the first mollified moment, which is obtained unconditionally, and finding a sharp upper bound for the higher mollified moments for these $L$-functions, under GRH. The proportion of non-vanishing is explicit, but extremely small.

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Ahmet M. Güloğlu, Hamza Yesilyurt. 2023-01-26. Mollified Moments of Cubic Dirichlet L-Functions over the Eisenstein Field. https://arxiv.org/abs/2301.10979

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