Euler constants from primes in arithmetic progression

2024/06/24 by Languasco, Alessandro, Moree, Pieter · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2406.16547

Abstract

Many Dirichlet series of number theoretic interest can be written as a product of generating series ζ _d,a(s)=∏_p≡ a\pmodd(1-p^-s)^-1, with p ranging over all the primes in the primitive residue class modulo a\pmodd, and a function H(s) well-behaved around s=1. In such a case the corresponding Euler constant can be expressed in terms of the Euler constants γ(d,a) of the series ζ _d,a(s) involved and the (numerically more harmless) term H'(1)/H(1). Here we systematically study γ(d,a), their numerical evaluation and discuss some examples.

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• Thinned Wallis-Type Prime Products in Residue Classes Modulo \(2^m\)

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