Asymptotic formulas for the logarithm of general L-functions at and near s=1

2024/01/31 by Kohji Matsumoto, Matsumoto, Kohji, Yumiko Umegaki +1
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2401.17610

openalex publication_date 2024/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a general form of L-function L(s) defined by an Euler product and satisfies several analytic assumptions. We show several asymptotic formulas for L(1) and log L(1). In particular those asymptotic formulas are valid for Dirichlet L-functions attached to almost all Dirichlet characters. Our theorems should be compared with former results due to Elliott, Montgomery and Weinberger, etc.

Related

• Monotonicity Results for Dirichlet L-functions
• On the validity of the Euler product inside the critical strip
• On moments of L-functions over Dirichlet characters
• The Dirichlet Problem for the Logarithmic Laplacian
• The Ratios conjecture for real Dirichlet characters and multiple Dirichlet series