Accurate Computations of Euler Products over Primes in Arithmetic Progressions

2019/11/25 by Olivier Ramaré, Ramaré, Olivier · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1911.10991

openalex publication_date 2019/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

This note provides truncated formulae with explicit error terms to compute Euler products over primes in arithmetic progressions of rational fractions. It further provides such a formula for the product of terms of the shape F(1/p, 1/p^s) when F is a two-variable polynomial with coefficients in ℂ and satisfying some restrictive conditions.

Cited by

• A central limit theorem for partitions involving generalised divisor functions

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• Fast multi-precision computation of some Euler products
• Explicit formulae for primes in arithmetic progressions, I
• Euler constants from primes in arithmetic progression
• Prime Values of the Euler Polynomial
• Euler's Function on Products of Primes in Progressions