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- 저자 : Guillarmou, Colin (검색결과 1 건)
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Eta invariant and Selberg zeta function of odd type over convex co-compact hyperbolic manifolds
Guillarmou, Colin,Moroianu, Sergiu,Park, Jinsung Elsevier 2010 Advances in mathematics Vol.225 No.5
<P><B>Abstract</B></P><P>We show meromorphic extension and give a complete description of the divisors of a Selberg zeta function of odd type ZΓ,Σo(λ) associated to the spinor bundle <I>Σ</I> on an odd dimensional convex co-compact hyperbolic manifold Γ\<SUP>H2n+1</SUP>. As a byproduct we do a full analysis of the spectral and scattering theory of the Dirac operator on asymptotically hyperbolic manifolds. We show that there is a natural eta invariant η(D) associated to the Dirac operator <I>D</I> over a convex co-compact hyperbolic manifold Γ\<SUP>H2n+1</SUP> and that exp(πiη(D))=ZΓ,Σo(0), thus extending Millson's formula to this setting. Under some assumption on the exponent of convergence of Poincaré series for the group <I>Γ</I>, we also define an eta invariant for the odd signature operator, and we show that for Schottky 3-dimensional hyperbolic manifolds it gives the argument of a holomorphic function which appears in the Zograf factorization formula relating two natural Kähler potentials for Weil–Petersson metric on Schottky space.</P>
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