Milnor-Selberg zeta functions and zeta regularizations

Details Milnor-Selberg zeta functions and zeta regularizations Milnor-Selberg zeta functions and zeta regularizations

2010-11-13

arxiv.org/abs/1011.3093v2

Mathematics

Number Theory

32 pages, 7 figures

Scientific paper

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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