An exact formula relating lattice points in symmetric spaces to the automorphic spectrum

zbMath1286.11083arXiv1104.5406MaRDI QIDQ2441062

Amy T. DeCelles

Publication date: 21 March 2014

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.5406

zbMATH Keywords

Sobolev spacelattice pointssymmetric spaceCasimir operatorautomorphic spectrumspectral transform

Mathematics Subject Classification ID

Other groups and their modular and automorphic forms (several variables) (11F55) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Lattice points in specified regions (11P21) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (1)

Global automorphic Sobolev theory and the automorphic heat kernel

Cites Work

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• Resolvent and lattice points on symmetric spaces of strictly negative curvature
• Integral moments of automorphic L-functions
• A lattice‐point problem in hyperbolic space
• Exponential Sums and Lattice Points III
• On Integration in Vector Spaces

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