On Differences of Zeta Values
Abstract
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, BaezDuarte, Voros and others. We apply the theory of NorlundRice integrals in conjunction with the saddle point method and derive precise asymptotic estimates. The method extends to Dirichlet Lfunctions and our estimates appear to be partly related to earlier investigations surrounding Li's criterion for the Riemann hypothesis.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2006
 DOI:
 10.48550/arXiv.math/0611332
 arXiv:
 arXiv:math/0611332
 Bibcode:
 2006math.....11332F
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 11M06;
 30B50;
 39A05;
 41A60
 EPrint:
 18 pages