Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 32 min ago
PreprintarXiv licencearXiv

The pseudo-Riemannian spectral zeta function density on scattering manifolds

  • Ashkan Sadat Kyaee
Open at sourcePDFDOICite

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 ε > 0, we consider complex powers (P± iε)−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.

Related

  1. Kernel Density Regression Estimation with Covariates on Riemannian Manifolds
    Gharbi Rihab, Salah Khardani, Mohamed Abdillahi Isman +1
    HALPreprintCC BY 4.0Full textStatisticsHAL
  2. On Polynomial Complex Hessian Equations I: Non-Linear Non-Spectral Elliptic Hessian Equations on Riemannian Manifolds
    Rémi Delloque
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsGeometry & topologyarXiv
  3. Spectral asymptotics of sub-Riemannian Laplacians on compact Heisenberg manifolds
    Sheng-Chen Mao, Ye Zhang
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsarXiv
  4. Riemannian Density-Driven Optimal Control: Tangent-Space LQR for Second-Order Multi-Agent Systems on Curved Manifolds
    Kooktae Lee, Ruchika Singh
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  5. Decomposing the spectral density function of an ARMA process
    Darlin Soto-Vásquez, Francisco Cuevas-Pacheco, Giovanni Motta +1
    arXivPreprintCC BY-SA 4.0Full textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{kyaee2026pseudoriemannian,
  title = {{The pseudo-Riemannian spectral zeta function density on scattering manifolds}},
  author = {Ashkan Sadat Kyaee},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05528},
  eprint = {2610.05528},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05528},
}
RIS
TY  - UNPB
TI  - The pseudo-Riemannian spectral zeta function density on scattering manifolds
AU  - Ashkan Sadat Kyaee
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05528
UR  - https://arxiv.org/abs/2610.05528
AB  - 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 ε > 0, we consider complex powers (P± iε)^−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.
ER  -