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Euler Products Beyond the Boundary |
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| Authors: | Taro Kimura Shin-ya Koyama Nobushige Kurokawa |
| Affiliation: | 1. Mathematical Physics Laboratory, RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama, 351-0198, Japan 2. Department of Biomedical Engineering, Toyo University, 2100 Kujirai, Kawagoe, Saitama, 350-8585, Japan 3. Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo, 152-8551, Japan |
| 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”, 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. |
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