February 26, 2024Open Access

Ratios conjecture of quartic L-functions of prime moduli

Key Points

Key points are not available for this paper at this time.

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.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Gao et al. (Mon,) studied this question.

synapsesocial.com/papers/68e779ebb6db6435876eea5f https://doi.org/https://doi.org/10.48550/arxiv.2402.17198

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli2024
2Ratios conjecture for quadratic twists of modular L-functions2024 · 1 citations
3Shifted moments of quadratic Dirichlet $L$-functions2024
4Wide moments of L-functions I : Twists by classgroup characters of imaginary quadratic fields2024 · 3 citations
5The first moment of central value of primitive quartic $L$-functions with fixed genus2025

Bookmark

View Full Paper