Mean value of cubic L-funcitons with fixed genus

2025/03/21 by Hong, Ziwei, Fang, Zhongqiu · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.17228

Abstract

We investigate the mean value of the first moment of primitive cubic L-functions over \mathbbF_q(T) in the non-Kummer setting. Specifically, we study the sum ∑_\substackχ primitive cubic
genus(χ)=gL_q((1)/(2), χ), where L_q(s,χ) denotes the L-function associated with primitive cubic character χ. Using double Dirichlet series, we derive an error term of size q^{((7)/(8)+ε)g}.

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