Quantum Chaos, Symmetry, and Zeta functions, II: Zeta Functions
نویسندگان
چکیده
منابع مشابه
Zeta Functions and Chaos
This paper is an expanded version of lectures given at M.S.R.I. in June of 2008. It provides an introduction to various zeta functions emphasizing zeta functions of a finite graph and connections with random matrix theory and quantum chaos. Section 2. Three Zeta Functions For the number theorist, most zeta functions are multiplicative generating functions for something like primes (or prime ide...
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Institute of Mathematics, Chinese Academy of Sciences, Beijing, P.R. China Department of Mathematics, University of California, Irvine, CA 92697-3875 [email protected] Abstract In this paper, we study the relation between the zeta function of a Calabi-Yau hypersurface and the zeta function of its mirror. Two types of arithmetic relations are discovered. This motivates us to formulate two genera...
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A q-analogue of the Hurwitz zeta-function is introduced through considerations on the spectral zeta-function of quantum group SUq(2), and its analytic aspects are studied via the Euler-MacLaurin summation formula. Asymptotic formulas of some relevant q-functions are discussed.
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Hilbert and Polya suggested that there might be a natural spectral interpretation of the zeroes of the Riemann Zeta function. While at the time there was little evidence for this, today the evidence is quite convincing. Firstly, there are the “function field” analogues, that is zeta functions of curves over finite fields and their generalizations. For these a spectral interpretation for their z...
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We review various periodic orbit formulae for the zeta function whose zeros represent semiclassical approximations to the energy levels of chaotic systems. In particular, we focus on the Riemann-Siegel-resummed expression. The emphasis is on the ability of such formulae to reproduce the analytic properties of the spetral determinant, whose zeros are the exact quantum levels. As an example, the ...
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ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 1997
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.1997.v1997.n1.a4