Infinite products involving Dirichlet characters and cyclotomic polynomials

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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Submitted on : Thursday, July 19, 2018 - 6:23:42 PM
Last modification on : Monday, November 26, 2018 - 1:53:30 PM

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K. Ditcher, Christophe Vignat. Infinite products involving Dirichlet characters and cyclotomic polynomials. Advances in Applied Mathematics, Elsevier, 2018, 100, pp.43 - 70. ⟨10.1016/j.aam.2018.05.003⟩. ⟨hal-01844864⟩

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