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Hessian of the Zeta Function for the Laplacian on Forms
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Kate Okikiolu
Published/Copyright:
July 27, 2005
Abstract
Let M be a compact closed n-dimensional manifold. Given a Riemannian metric on M, we consider the zeta functions Z(s) for the de Rham Laplacian and the Bochner Laplacian on p-forms. The hessian of Z(s) with respect to variations of the metric is given by a pseudodi erential operator Ts. When the real part of s is less than n/2−1 we compute the principal symbol of Ts. This can be used to determine whether a general critical metric for (d/ds)kZ(s) has finite index, or whether it is an essential saddle point.
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Published Online: 2005-07-27
Published in Print: 2005-01-01
© de Gruyter
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Articles in the same Issue
- On the Trace of Hecke Operators for Maass Forms for Congruence Subgroups II
- Approximating L2-Signatures by Their Compact Analogues
- Preservation of Perfectness and Acyclicity: Berrick and Casacuberta's Universal Acyclic Space Localized at a Set of Primes
- On Certain Functional and Partial Differential Equations
- Spectral Asymptotics of Generalized Measure Geometric Laplacians on Cantor Like Sets
- Hessian of the Zeta Function for the Laplacian on Forms
- Global Existence of Solutions to Multiple Speed Systems of Quasilinear Wave Equations in Exterior Domains
