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arXiv:math/0703508 [math.NT]AbstractReferencesReviewsResources

Generalized Euler constants

Harold G. Diamond, Kevin Ford

Published 2007-03-17, updated 2007-07-07Version 2

We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent monotonicity is investigated. We also prove that a certain property of these numbers is equivalent to the Riemann Hypothesis.

Comments: v2. 13 pages. Minor changes suggested by the referee. To appear in Math. Proc. Cambridge Phil. Soc
Journal: Math. Proc. Cambridge Phil. Soc 145 (2008), 27-41
Categories: math.NT
Subjects: 11N25, 11N35
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