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Milnor-Selberg zeta functions and zeta regularizations

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概要 By a similar idea for constructing Milnor's gamma functions, we study "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. Moreover, 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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MI2010-34 pdf 452 KB 106  

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登録日 2012.12.26
更新日 2015.11.06