Effective hybrid joint universality for Dirichlet L-functions and its application

2025/12/02 by Keita Nakai, Nakai, Keita
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2512.02428

Abstract

In 2003, Garunkštis provided a lower bound for the lower density of the universality theorem for the Riemann zeta-function. In this paper, we generalize this result for the hybrid joint universality theorem for Dirichlet L-functions whose moduli are prime numbers. Furthermore, by its application, we estimate a lower bound of the lower density of the universality theorem for Hurwitz zeta-functions with rational parameters.

Citations

• Limit theorem for the hybrid joint universality theorem on zeta and L-functions
• Effective Weak Universality in Short Intervals
• New developments toward the Gonek Conjecture on the Hurwitz zeta-function
• Effective uniform approximation by L-functions in the Selberg class
• An effective universality theorem for the Riemann zeta function
• A survey on the theory of universality for zeta and L-functions

Related

• Limit theorem for the hybrid joint universality theorem on zeta and L-functions
• Discrete universality, continuous universality and hybrid universality are equivalent
• Joint Universality for the Riemann zeta-function with general shifts
• A survey on the theory of universality for zeta and L-functions
• On mixed joint discrete universality for a class of zeta-functions III