On the constants in Mertens' theorems for primes in arithmetic progressions

arXiv2306.09981MaRDI QIDQ6440562

Daniel Keliher, Ethan Simpson Lee

Publication date: 16 June 2023

Abstract: A 1976 result from Norton may be used to give an asymptotic (but not explicit) description of the constant in Mertens' second theorem for primes in arithmetic progressions. Assuming the Generalised Riemann Hypothesis, we make Norton's observation explicit and extend this result to multiple progressions.

Has companion code repository: https://github.com/ethanslee/on-the-constants-in-mertens-theorems-for-primes-in-arithmetic-progressions

Mathematics Subject Classification ID

Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Primes in congruence classes (11N13)

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