Ratios conjecture of cubic L-functions of prime moduli

2023/11/15 by Peng Gao, Liangyi Zhao, Gao, Peng +1
Mathematics · Computer Science · #Analytic Number Theory Research #Algebraic Geometry and Number Theory #Coding theory and cryptography

paper · pdf · doi:10.1016/j.indag.2025.07.001

Abstract

We develop L -functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of cubic Hecke L -functions of prime moduli over the Eisenstein field using multiple Dirichlet series under the generalized Riemann hypothesis. As applications, we evaluate asymptotically the first moment of central values as well as the one-level density of the same family of L -functions.

Citations

• Applications of theL-functions ratios conjectures

Related

• Ratios conjecture of quadratic Hecke L-functions of prime-related moduli
• Ratios conjecture of quartic L-functions of prime moduli
• Ratios conjecture for primitive quadratic Hecke L-functions
• The Ratios conjecture for real Dirichlet characters and multiple Dirichlet series
• Mollified Moments of Cubic Dirichlet L-Functions over the Eisenstein Field