On Differences of Zeta Values

Details On Differences of Zeta Values On Differences of Zeta Values

2006-11-11

arxiv.org/abs/math/0611332v2

Mathematics

Classical Analysis and ODEs

18 pages

Scientific paper

10.1016/j.cam.2007.07.040

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.

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