Euler Products beyond the Boundary
Number Theory
2014-02-05 v5 Statistical Mechanics
Abstract
We investigate the behavior of the Euler products of the Riemann zeta function and Dirichlet L-functions on the critical line. A refined version of the Riemann hypothesis, which is named "the Deep Riemann Hypothesis" (DRH), is examined. We also study various analogs for global function fields. We give an interpretation for the nontrivial zeros from the viewpoint of statistical mechanics.
Cite
@article{arxiv.1210.1216,
title = {Euler Products beyond the Boundary},
author = {Taro Kimura and Shin-ya Koyama and Nobushige Kurokawa},
journal= {arXiv preprint arXiv:1210.1216},
year = {2014}
}
Comments
16 pages, 20 figures; discussion in Sec. 3 extended; references added; figures and discussion added; references added