منابع مشابه
Higher moments of the Epstein zeta functions
holds as T → ∞. The basic tools of them are the approximate functional equations for ζ(s) and ζ(s). Therefore, one might think that we can obtain the asymptotic formula for the higher moments (sixth moment, eighth moment, etc· · · ) of ζ(s) on the critical line Re(s) = 12 by using the approximate functional equations for ζ(s) (k ≥ 3). However, although these approximate functional equations are...
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In this paper, we generalize the zeta function for a fractal string (as in [18]) in several directions. We first modify the zeta function to be associated with a sequence of covers instead of the usual definition involving gap lengths. This modified zeta function allows us to define both a multifractal zeta function and a zeta function for higher-dimensional fractal sets. In the multifractal ca...
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We consider a generalization of the Mahler measure of a multivariable polynomial P as the integral of log |P | in the unit torus, as opposed to the classical definition with the integral of log |P |. A zeta Mahler measure, involving the integral of |P |s, is also considered. Specific examples are computed, yielding special values of zeta functions, Dirichlet L-functions, and polylogarithms.
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On an open manifold, the spaces of metrics or connections of bounded geometry, respectively, split into an uncountable number of components. We show that for a pair of metrics or connections, belonging to the same component, relative ζ-functions, determinants, torsion for pairs of generalized Dirac operators are well defined.
متن کاملSelberg zeta functions for spaces of higher rank
5 Introduction In 1956 A. Selberg introduced the zeta function Z(s) = c N ≥0 (1 − e −(s+N)l(c)), Re(s) >> 0, where the first product is taken over all primitive closed geodesics in a compact Riemannian surface of genus ≥ 2, equipped with the hyperbolic metric, and l(c) denotes the length of the geodesic c. Selberg proved that the product converges if the real part of s is large enough and that ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1995
ISSN: 0001-8708
DOI: 10.1006/aima.1995.1004