Zeta zeros and Dirichlet L-functions
type: Item
instance of: scholarly article
title: Zeta zeros and Dirichlet L-functions
zbMATH Open document ID: 0663.10044
author: Akio Fujii
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: The author continues his earlier work on the uniformity of distribution of zeros of the Riemann zeta-function and Dirichlet L-functions [Comment. Math. Univ. St. Pauli 31, 99-113 (1982; Zbl 0489.10032) and Proc. Japan Acad., Ser. A 63, 370-373 (1987; Zbl 0636.10032)]. He assumes the Riemann hypothesis and proves three theorems. The first evaluates a certain sum of values of Dirichlet L-functions over imaginary parts of zeros of \(\zeta\) (s). The second theorem specializes the result of the first to \(\rho\) (s). It states that, for any fixed integer \(K\geq 2\), \[ \lim_{T\to \infty}2\pi T^{-1}\sum_{0<\gamma \leq T}(\zeta (\frac{1}{2}+\frac{i\gamma}{K})-1)=\frac{\zeta '}{\zeta}(\frac{K+1}{2}). \] The third theorem gives a relation equivalent to the Generalized Riemann Hypothesis for all Dirichlet functions L(s,\(\chi)\).
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 4083744
zbMATH Keywords: uniform distribution of zeros
zbMATH Keywords: approximate functional equation
zbMATH Keywords: Riemann zeta-function
zbMATH Keywords: Dirichlet L-functions
zbMATH Keywords: Generalized Riemann Hypothesis
reviewed by: Aleksandar Ivić
MaRDI profile type: Publication
full work available at URL: pjaa.64.215
OpenAlex ID: W4253595031
cites work: Q3950641
cites work: Uniform distribution of the zeros of the Riemann zeta function and the mean value theorems of Dirichlet L-functions
cites work: Q5554455
cites work: Q5791262
cites work: Вертикальные распределения нулей дзета-функции и расширенная гипотеза Римана
DOI: 10.3792/PJAA.64.215
description: scientific article; zbMATH DE number 4083744