TY - JOUR
T1 - Milnor-Selberg zeta functions and zeta regularizations
AU - Kurokawa, Nobushige
AU - Wakayama, Masato
AU - Yamasaki, Yoshinori
N1 - Funding Information:
The second author was partially supported by Grant-in-Aid for Scientific Research (B) No. 21340011 . The third author was partially supported by Grant-in-Aid for Young Scientists (B) No. 21740019 .
PY - 2013/2
Y1 - 2013/2
N2 - By a similar idea for the construction of Milnor's gamma functions, we introduce "higher depth determinants" of the Laplacian on a compact Riemann surface of genus greater than one. We prove that, as a generalization of the determinant expression of the Selberg zeta function, this higher depth determinant can be expressed as a product of multiple gamma functions and what we call a Milnor-Selberg zeta function. It is shown that the Milnor-Selberg zeta function admits an analytic continuation, a functional equation and, remarkably, has an Euler product.
AB - By a similar idea for the construction of Milnor's gamma functions, we introduce "higher depth determinants" of the Laplacian on a compact Riemann surface of genus greater than one. We prove that, as a generalization of the determinant expression of the Selberg zeta function, this higher depth determinant can be expressed as a product of multiple gamma functions and what we call a Milnor-Selberg zeta function. It is shown that the Milnor-Selberg zeta function admits an analytic continuation, a functional equation and, remarkably, has an Euler product.
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U2 - 10.1016/j.geomphys.2012.10.015
DO - 10.1016/j.geomphys.2012.10.015
M3 - Article
AN - SCOPUS:84875255423
SN - 0393-0440
VL - 64
SP - 120
EP - 145
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
IS - 1
ER -