Euler Products beyond the Boundary
arXiv:1210.1216 · doi:10.1007/s11005-013-0644-3
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.
16 pages, 20 figures; discussion in Sec. 3 extended; references added; figures and discussion added; references added