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arXiv · 2402.17198

Ratios conjecture of quartic $L$-functions of prime moduli

Peng Gao·Liangyi Zhao
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Abstract

We apply the method of multiple Dirichlet series to develop $L$-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for the family of quartic Hecke $L$-functions of prime moduli over the Gaussian field under the generalized Riemann hypothesis. As consequences, we evaluate asymptotically the first moment of central values as well as the one-level density of the same family of $L$-functions.

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Peng Gao, Liangyi Zhao. 2024-02-27. Ratios conjecture of quartic $L$-functions of prime moduli. https://arxiv.org/abs/2402.17198

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