Computational strategies for the Riemann zeta function

2000/09/01 by Jonathan M. Borwein, David M. Bradley, Richard E. Crandall · 8 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical functions and polynomials

paper · pdf · doi:10.1016/s0377-0427(00)00336-8

crossref issued 2000/09/01 · crossref published 2000/09/01 · crossref published-print 2000/09/01 · openalex publication_date 2000/09/01 · crossref created 2002/07/25 · crossref deposited 2021/05/06 · openalex created_date 2025/10/10 · crossref indexed 2026/07/27 · openalex updated_date 2026/07/31

Citations

• On a positivity property of the Riemann ξ-function
• Sur la distribution des nombres premiers
• Irregular Primes and Cyclotomic Invariants to 12 Million
• Fast Fourier Transforms for Nonequispaced Data
• Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind
• The Positivity of a Sequence of Numbers and the Riemann Hypothesis
• Fast Multiple-Precision Evaluation of Elementary Functions
• Prime Numbers and Computer Methods for Factorization

Cited by

• On the Random Character of Fundamental Constant Expansions
• Random Generators and Normal Numbers
• A sharp region where 𝜋(𝑥)-fc(r) is positive
• Log-sine-polylog integrals and alternating Euler sums
• An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions
• Clausen function [wikipedia]
• Euler's constant [wikipedia]
• Riemann zeta function [wikipedia]