Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1895915 | Journal of Geometry and Physics | 2013 | 26 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Nobushige Kurokawa, Masato Wakayama, Yoshinori Yamasaki,