A unified strategy to compute some special functions of number-theoretic interest

DOI10.1016/j.jnt.2022.12.003OpenAlexW4319991247MaRDI QIDQ2689521

Alessandro Languasco

Publication date: 10 March 2023

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.07686

zbMATH Keywords

Euler gamma-functionCatalan constantBateman \(G\)-functiondigamma and polygamma functionsDirichlet \(L\)-functions and \(\beta\)-functionHurwitz zeta-function and \(\eta\)-function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Computation of special functions and constants, construction of tables (65D20) Software, source code, etc. for problems pertaining to number theory (11-04) Hurwitz and Lerch zeta functions (11M35) Numerical approximation and evaluation of special functions (33F05)

Related Items (1)

Numerical estimates on the Landau-Siegel zero and other related quantities

Uses Software

• PARI/GP
• FXT
• hfloat

Cites Work

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• Efficient computation of the Euler-Kronecker constants of prime cyclotomic fields
• Numerical verification of Littlewood's bounds for \(|L(1,\chi)|\)
• Euler’s constant: Euler’s work and modern developments
• The Accuracy of Floating Point Summation
• The Mathematical-Function Computation Handbook
• A Stochastic Approach to the Gamma Function
• Matters Computational
• A fast algorithm to compute the Ramanujan-Deninger gamma function and some number-theoretic applications
• An Algorithm for the Machine Calculation of Complex Fourier Series
• Number Theory

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