Analytic torsion and Ruelle zeta functions for hyperbolic manifolds with cusps |
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Authors: | Jinsung Park |
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Affiliation: | School of Mathematics, Korea Institute for Advanced Study, Hoegiro 87, Dongdaemun-gu, Seoul 130-722, Republic of Korea |
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Abstract: | In this paper we derive a relationship of the leading coefficient of the Laurent expansion of the Ruelle zeta function at s=0 and the analytic torsion for hyperbolic manifolds with cusps. Here, the analytic torsion is defined by a certain regularized trace following Melrose [R.B. Melrose, The Atiyah-Patodi-Singer Index Theorem, Res. Notes Math., vol. 4, A.K. Peters, Ltd., Wellesley, MA, 1993]. This extends the result of Fried, which was proved for the compact case in [D. Fried, Analytic torsion and closed geodesics on hyperbolic manifolds, Invent. Math. 84 (3) (1986) 523-540], to a noncompact case. |
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Keywords: | Analytic torsion Ruelle zeta function Selberg trace formula |
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