Alternating Euler sums at the negative integers

Details Alternating Euler sums at the negative integers Alternating Euler sums at the negative integers

2008-11-26

arxiv.org/abs/0811.4437v1

Mathematics

Number Theory

15 pages, To appear in the Hardy-Ramanujan journal

Scientific paper

We study three special Dirichlet series, two of them alternating, related to
the Riemann zeta function. These series are shown to have extensions to the
entire complex plane and we find their values at the negative integers (or
residues at poles). These values are given in terms of Bernoulli and Euler
numbers.

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