Euler Products beyond the Boundary

Taro Kimura, Shin-ya Koyama, Nobushige Kurokawa

Published 2012-10-03, updated 2013-07-16Version 5

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.