On Differences of Zeta Values

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Finite differences of values of the Riemann zeta function at the integers are explored. Such quantities, which occur as coefficients in Newton series representations, have surfaced in works of Maslanka, Coffey, Baez-Duarte, Voros and others. We apply the theory of Norlund-Rice integrals in conjunction with the saddle point method and derive precise asymptotic estimates. The method extends to Dirichlet L-functions and our estimates appear to be partly related to earlier investigations surrounding Li's criterion for the Riemann hypothesis.
18 pages

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Classical Analysis and ODEs, 11M06; 30B50; 39A05; 41A60

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http://salesiana.dossiersoluciones.com/handle/123456789/169330

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611332
 http://arxiv.org/abs/math/0611332
 doi:10.1016/j.cam.2007.07.040

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arXiv