✦ LIBER ✦

On differences of zeta values

✍ Scribed by Philippe Flajolet; Linas Vepstas

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 485 KB
Volume: 220
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.07.040

No coin nor oath required. For personal study only.

✦ Synopsis

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 Bombieri-Lagarias, Maślanka, Coffey, Báez-Duarte, Voros and others. We apply the theory of Nörlund-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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