Generalized Euler constants

Details Generalized Euler constants Generalized Euler constants

2007-03-17

arxiv.org/abs/math/0703508v2

Math. Proc. Cambridge Phil. Soc 145 (2008), 27-41

Mathematics

Number Theory

v2. 13 pages. Minor changes suggested by the referee. To appear in Math. Proc. Cambridge Phil. Soc

Scientific paper

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.

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