On the distribution of log |L(σ, χ)| and log L(σ, χ_D) in the modulus aspect

2024/10/27 by M. Hosoi, Hosoi, Manami, Yumiko Umegaki +1
Mathematics · #11M06 #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2410.20341

openalex publication_date 2024/10/27 · openalex created_date 2024/11/15 · openalex updated_date 2026/07/28

Abstract

Let χ be a primitive Dirichlet character whose conductor q is a prime number. For the certain averages of values of log |L(s, χ)| in q-aspect at a fixed s=σ>1/2, under Generalized Riemann Hypothesis (GRH), we explain it can be written as integrals involving the same density function (M-function) for the average of values of the difference between the logarithms of two symmetric power L-functions in the level aspect. For the distribution of values of log L(s, χ_D) and L'/L(s, χ_D) in the D-aspect at a fixed s=σ>1/2 which L(σ', χ)≠ 0 in σ≤ σ' ≤ 1, where χ_D is a real character attached to a fundamental discriminant D, we construct a M-function unconditionally.

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