Counting zeros of Dirichlet $L$-functions

DOI10.1090/mcom/3599zbMath1475.11148arXiv2005.02989OpenAlexW3093614117MaRDI QIDQ5856750

Greg Martin, Kevin O'Bryant, Michael A. Bennett, Andrew Rechnitzer

Publication date: 29 March 2021

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.02989

zbMATH Keywords

Dirichlet \(L\)-functions

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Algebraic number theory computations (11Y40) Real zeros of (L(s, chi)); results on (L(1, chi)) (11M20) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Primes in congruence classes (11N13) Analytic computations (11Y35)

Related Items (3)

Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis ⋮ Counting zeros of the Riemann zeta function ⋮ Medium-sized values for the prime number theorem for primes in arithmetic progressions

Uses Software

• PARI/GP

Cites Work

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• Explicit bounds for primes in arithmetic progressions
• On the Phragmén-Lindelöf theorem and some applications
• An improved upper bound for the argument of the Riemann zeta-function on the critical line. II
• Explicit Estimates for the Error Term in the Prime Number Theorem for Arithmetic Progressions
• Computing the Principal Branch of log-Gamma
• ON THE ACCURACY OF ASYMPTOTIC APPROXIMATIONS TO THE LOG-GAMMA AND RIEMANN–SIEGEL THETA FUNCTIONS
• An improved upper bound for the error in the zero-counting formulae for Dirichlet $L$-functions and Dedekind zeta-functions
• Numerical computations concerning the GRH

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