Automorphic Hamiltonians, Epstein zeta functions, and Kronecker limit formulas

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Automorphic Hamiltonians, Epstein zeta functions, and Kronecker limit formulas

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Sands, Adrienne

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2020-09

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Abstract

We construct an automorphic Hamiltonian which has purely discrete spectrum on $L^2\left(SL_r(\Z)\backslash SL_r(\R)/SO(r,\R)\right)$, identify its ground state, and show how it can characterize a nuclear Fr\'echet automorphic Schwartz space.

Keywords

Automorphic forms

Automorphic Hamiltonian

Automorphic Schwartz space

Degenerate Eisenstein series

Epstein zeta functions

Description

University of Minnesota Ph.D. dissertation. 2020. Major: Mathematics. Advisor: Paul Garrett. 1 computer file (PDF); 92 pages.

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Sands, Adrienne. (2020). Automorphic Hamiltonians, Epstein zeta functions, and Kronecker limit formulas. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/217155.

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