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This is a Quantitative Study study.

October 19, 2025Open Access

The first moment of central value of primitive quartic L-functions with fixed genus

Key Points

The mean value of the first moment of primitive quartic L-functions was analyzed.
Key findings include an error term of size q^(3/5+ε)g associated with these L-functions.
The methodology involved the use of double Dirichlet series for deriving the results.
This study highlights the implications in the non-Kummer setting and the significance of the genus.

Abstract

We investigate the mean value of the first moment of primitive quartic L-functions over Fq (T) in the non-Kummer setting. Specifically, we study the sum equation* ⏦ ₏ₑ₈₌₈ₓ₈ₕ₄\ ₐₔ₀ₑₓ₈₂\\ ⏦ℂ ₏ₑ₈₌₈ₓ₈ₕ₄\\ ₆₄₍ₔₒ (⏦) =₆Lq (12, χ), equation* where Lq (s, χ) denotes the L-function associated with primitive quartic character χ. Using double Dirichlet series, we derive an error term of size q^ (3{5+) g}.

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Cite This Study

Ziwei Hong (Sat,) studied this question.

synapsesocial.com/papers/68f43f09854d1061a58ac9e2 https://doi.org/https://doi.org/10.48550/arxiv.2504.14291

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