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Generalized Euler constants

Published online by Cambridge University Press:  01 July 2008

HAROLD G. DIAMOND  and
KEVIN FORD
HAROLD G. DIAMOND
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, IL 61801, USA. e-mail: [email protected], [email protected]
KEVIN FORD
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, IL 61801, USA. e-mail: [email protected], [email protected]
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Abstract

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

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 27 - 41
Copyright
Copyright © Cambridge Philosophical Society 2008

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