TY - JOUR
T1 - Euler Products Beyond the Boundary
AU - Kimura, Taro
AU - Koyama, Shin ya
AU - Kurokawa, Nobushige
N1 - Funding Information:
Taro Kimura: Partially supported by JSPS Research Fellowships for Young Scientists (Nos. 23-593, 25-4302).
PY - 2014/1
Y1 - 2014/1
N2 - 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.
AB - 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.
KW - Dirichlet L-functions
KW - Euler products
KW - the Riemann hypothesis
KW - the Riemann zeta function
KW - the generalized Riemann hypothesis
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U2 - 10.1007/s11005-013-0644-3
DO - 10.1007/s11005-013-0644-3
M3 - Article
AN - SCOPUS:84891513893
SN - 0377-9017
VL - 104
SP - 1
EP - 19
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 1
ER -