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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Advances in Applied Mathematics, Elsevier, 2018, 100, pp.43 - 70. 〈10.1016/j.aam.2018.05.003〉
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Contributeur : Christophe Vignat <>
Soumis le : jeudi 19 juillet 2018 - 18:23:42
Dernière modification le : lundi 26 novembre 2018 - 13:53:30

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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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