ON THE ACCURACY OF ASYMPTOTIC APPROXIMATIONS TO THE LOG-GAMMA AND RIEMANN–SIEGEL THETA FUNCTIONS

DOI10.1017/S1446788718000393zbMath1436.11106arXiv1609.03682OpenAlexW3101695955WikidataQ60321102 ScholiaQ60321102MaRDI QIDQ4972093

Richard P. Brent

Publication date: 22 November 2019

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.03682

zbMATH Keywords

gamma functionRiemann zeta functionasymptoticslog-gamma functionRiemann-Siegel theta function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Computation of special functions and constants, construction of tables (65D20) Elementary classical functions (33B99)

Related Items (2)

Accurate estimation of sums over zeros of the Riemann zeta-function ⋮ Counting zeros of Dirichlet $L$-functions

Uses Software

• DLMF

Cites Work

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• DLMF
• Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials
• Computational strategies for the Riemann zeta function
• Generalization of Binet's Gamma function formulas
• Extended computation of the Riemann zeta‐function
• On the Zeros of the Riemann Zeta Function in the Critical Strip
• On the Zeros of the Riemann Zeta Function in the Critical Strip. II
• Computing the Principal Branch of log-Gamma
• A Simple Explanation of the Stokes Phenomenon
• The Riemann-Siegel expansion for the zeta function: high orders and remainders
• Stokes Phenomenon and Matched Asymptotic Expansions
• Calculation of the Gamma Function by Stirling's Formula

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