On the linear independence of the special values of a Dirichlet series with periodic coefficients

Details On the linear independence of the special values of a Dirichlet series with periodic coefficients On the linear independence of the special values of a Dirichlet series with periodic coefficients

2011-02-16

arxiv.org/abs/1102.3247v1

Mathematics

Number Theory

30 pages

Scientific paper

A lower bound for the dimension of the $\Q$-vector space spanned by special values of a Dirichlet series with periodic coefficients is given. As a corollary, it is deduced that both special values at even integers and at odd integers contain infinitely many irrational numbers. This result is proved by T.Rivoal if the function considered is the Riemann zeta function, and this paper gives its generalization to more general Dirichlet series.

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