Designing Poincare Series for Number Theoretic Applications
Number Theory
2014-01-09 v1 Representation Theory
Abstract
The Poincar\'{e} series giving the subconvexity results of Diaconu and Garrett is the solution to an automorphic partial differential equation, constructed by winding-up the solution to the corresponding differential equation on the free space. Generalizing this approach allows design of higher rank Poincar\'{e} series with specific number theoretic applications in mind: a Poincar\'{e} series for producing an explicit formula for the number of lattice points in an expanding region in a symmetric space, a Poincar\'{e} series producing moments of L-functions, and a Poincar\'{e} series designed for applications involving pseudo-Laplacians.
Keywords
Cite
@article{arxiv.1401.1780,
title = {Designing Poincare Series for Number Theoretic Applications},
author = {Amy T. DeCelles},
journal= {arXiv preprint arXiv:1401.1780},
year = {2014}
}
Comments
17 pages, supercedes arxiv:1104.4313. arXiv admin note: substantial text overlap with arXiv:1104.5406