Ratios conjecture of quartic L-functions of prime moduli

2024/02/27 by Peng Gao, Liangyi Zhao, Gao, Peng +1
Mathematics · #Analytic Number Theory Research #Algebraic Geometry and Number Theory #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2402.17198

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.

Related

• Ratios conjecture of cubic L-functions of prime moduli
• Ratios conjecture of quadratic Hecke L-functions of prime-related moduli
• Ratios conjecture for primitive quadratic Hecke L-functions
• The Ratios conjecture for real Dirichlet characters and multiple Dirichlet series
• Low-lying zeros of a family of quadratic Hecke L-functions via ratios conjecture