%0 Conference Proceedings
%T Zeta functions over zeros of Zeta functions and an exponential-asymptotic view of the Riemann Hypothesis
%+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT)
%A Voros, André
%F Invité
%< avec comité de lecture
%( RIMS Kôkyûroku Bessatsu
%B Exponential analysis of differential equations and related topics
%C Kyoto, Japan
%Y Y. Takei
%I RIMS, Kyoto University
%V B52
%P 147-164
%8 2013-10-15
%D 2013
%Z 1403.4558
%Z MSC 11-02, 11-06, 11M26, 11M41, 11M35, 30B40, 30E15, 41A60
%Z Mathematics [math]Conference papers
%X We review generalized zeta functions built over the Riemann zeros (in short: "superzeta" functions). They are symmetric functions of the zeros that display a wealth of explicit properties, fully matching the much more elementary Hurwitz zeta function. As a concrete application, a superzeta function enters an integral repre-sentation for the Keiper–Li coefficients, whose large-order behavior thereby becomes computable by the method of steepest descents; then the dominant saddle-point en-tirely depends on the Riemann Hypothesis being true or not, and the outcome is a sharp exponential-asymptotic criterion for the Riemann Hypothesis that only refers to the large-order Keiper–Li coefficients. As a new result, that criterion, then Li's criterion, are transposed to a novel sequence of Riemann-zeta expansion coefficients based at the point 1/2 (vs 1 for Keiper–Li).
%G English
%2 https://cea.hal.science/cea-01076225/document
%2 https://cea.hal.science/cea-01076225/file/1403.4558v2.pdf
%L cea-01076225
%U https://cea.hal.science/cea-01076225
%~ CEA
%~ CNRS
%~ INSMI
%~ DSM-IPHT
%~ CEA-DRF
%~ GS-MATHEMATIQUES
%~ GS-PHYSIQUE