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Article Dans Une Revue Advances in Applied Mathematics Année : 2018

Infinite products involving Dirichlet characters and cyclotomic polynomials

Résumé

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.

Dates et versions

hal-01844864 , version 1 (19-07-2018)

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