Infinite products involving Dirichlet characters and cyclotomic polynomials

2018/01/28 by Dilcher, K., Vignat, C.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1801.09160

Abstract

Using some basic properties of the gamma function, we evaluate a simple class of infinite products involving Dirichlet characters as a finite product of gamma functions and, in the case of odd characters, as a finite product of sines. As a consequence we obtain evaluations of certain multiple L-series. In the final part of this paper we derive expressions for infinite products of cyclotomic polynomials, again as finite products of gamma or of sine functions.

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