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Global Automorphic Sobolev Theory and The Automorphic Heat Kernel
Amy T. DeCelles
Heat kernels arise in a variety of contexts including probability, geometry, and functional analysis; the automorphic heat kernel is particularly important in number theory and str…
Designing Poincare Series for Number Theoretic Applications
Amy T. DeCelles
The Poincaré series giving the subconvexity results of Diaconu and Garrett is the solution to an automorphic partial differential equation, constructed by winding-up the sol…
Branching of Automorphic Fundamental Solutions
Amy T. DeCelles
Automorphic fundamental solutions and, more generally, solutions of automorphic differential equations, play a key role in the Diaconu-Garrett-Goldfeld prescription for spectral id…
An exact formula relating lattice points in symmetric spaces to the automorphic spectrum
Amy DeCelles
We extract an exact formula relating the number of lattice points in an expanding region of a complex semi-simple symmetric space and the automorphic spectrum from a spectral ident…