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arXiv · 1801.09160

Infinite products involving Dirichlet characters and cyclotomic polynomials

K. Dilcher·C. Vignat
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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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K. Dilcher, C. Vignat. 2018-01-28. Infinite products involving Dirichlet characters and cyclotomic polynomials. https://arxiv.org/abs/1801.09160

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