On ``\(M\)-functions closely related to the distribution of \(L'/L\)-values

DOI10.2977/prims/1216238306zbMath1168.11031OpenAlexW2156627512MaRDI QIDQ2518198

Yasutaka Ihara

Publication date: 15 January 2009

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1216238306

zbMATH Keywords

\(L\)-functionsBessel functionsdensity functionEuler product

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) (zeta (s)) and (L(s, chi)) (11M06) Other Dirichlet series and zeta functions (11M41) Zeta functions and (L)-functions of number fields (11R42)

Related Items (16)

An asymptotic formula for the \(2k\)-th power mean value of \(|(L^{\prime}/L)(1+it_0, \chi)|\) ⋮ On the value-distribution of the difference between logarithms of two symmetric power L-functions ⋮ On the Value-Distribution of Logarithmic Derivatives of Dirichlet L-Functions ⋮ Small Values of |L'/L(1,χ)| ⋮ Large deviations for values of \(L\)-functions attached to cusp forms in the level aspect ⋮ The value-distribution of Artin \(L\)-functions associated with cubic fields in conductor aspect ⋮ An M-function associated with Goldbach's problem ⋮ Integral operators arising from the Riemann zeta function ⋮ Efficient computation of the Euler-Kronecker constants of prime cyclotomic fields ⋮ The density function for the value-distribution of the Lerch zeta-function and its applications ⋮ On certain arithmetic functions \(\tilde M(s; z_{1}; z_{2})\) associated with global fields: analytic properties ⋮ On certain mean values of logarithmic derivatives of \(L\)-functions and the related density functions ⋮ A fast algorithm to compute the Ramanujan-Deninger gamma function and some number-theoretic applications ⋮ On \(M\)-functions for the value-distributions of \(L\)-functions ⋮ Irregular Behaviour of Class Numbers and Euler-Kronecker Constants of Cyclotomic Fields: The Log Log Log Devil at Play ⋮ Nearest neighbor spacing distributions for the zeros of the real or imaginary part of the Riemann xi-function on vertical lines

Cites Work

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• Asymptotic probability measures of zeta-functions of algebraic number fields
• On the logarithmic derivatives of Dirichlet L-functions at s=1
• On the Euler-Kronecker constants of global fields and primes with small norms
• Distribution Functions and the Riemann Zeta Function

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