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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 generaliz...ation 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.続きを見る
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Mendeley出力
