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arXiv · 2610.05528

The pseudo-Riemannian spectral zeta function density on scattering manifolds

Ashkan Sadat Kyaee
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Abstract

We study spectral zeta densities associated with complex powers of principally scalar Laplace-type operators on pseudo-Riemannian scattering spaces of mixed signature and arbitrary dimension. The construction extends, beyond the even-dimensional Lorentzian case, the local analysis of Feynman complex powers developed by Dang and Wrochna. Namely, for $\varepsilon > 0$, we consider complex powers $(P\pm i\varepsilon)^{-α}$ and prove that the diagonal trace densities admit meromorphic continuation. We relate their poles to local geometric invariants, in particular to the pseudo-Riemannian scalar curvature. Our proof combines uniform Feynman resolvent estimates with a direct analysis of the Hadamard parametrix in pseudo-Riemannian signature. Beyond the Lorentzian case, the use of causal convexity is replaced by a geometric no-return argument.

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Ashkan Sadat Kyaee. 2026-10-04. The pseudo-Riemannian spectral zeta function density on scattering manifolds. https://arxiv.org/abs/2610.05528

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