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

2011/02/16 by Masaki Nishimoto, Nishimoto, Masaki · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1102.3247

30 pages

arxiv created 2011/02/16 · arxiv updated 2011/02/17

Abstract

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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