Author:
Serrano Holgado Álvaro,Navas Vicente Luis Manuel
Abstract
AbstractWe consider a Dirichlet series $$\sum _{n=1}^{\infty } a_{n}^{-s}$$
∑
n
=
1
∞
a
n
-
s
where $$a_{n}$$
a
n
satisfies a linear recurrence of arbitrary degree with integer coefficients. Under suitable hypotheses, we prove that it has a meromorphic continuation to the complex plane, giving explicit formulas for its pole set and residues, as well as for its finite values at negative integers, which are shown to be rational numbers. To illustrate the results, we focus on some concrete examples which have also been studied previously by other authors.
Funder
Ministerio de Ciencia e Innovación
Publisher
Springer Science and Business Media LLC
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