Generalized Euler constants

Harold G. Diamond; Kevin Ford

doi:10.1017/S0305004108001187

Generalized Euler constants

Harold G. Diamond, Kevin Ford

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the distribution of a family {γ(P)} of generalized Euler constants arising from integers sieved by finite sets of primes P. For P=P _r, the set of the first r primes, γ(P_r) → exp(-γ) as r → ∞. Calculations suggest that γ(P _r) is monotonic in r, but we prove it is not. Also, we show a connection between the distribution of γ(P_r) - exp(-γ) and the Riemann hypothesis.

Original language	English (US)
Pages (from-to)	27-41
Number of pages	15
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	145
Issue number	1
DOIs	https://doi.org/10.1017/S0305004108001187
State	Published - Jul 2008

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General Mathematics

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Generalized Euler constants

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