Heat kernels, Bergman kernels, and cusp forms
Number Theory
2015-07-06 v2
Abstract
In this article, we describe a geometric method to study cusp forms, which relies on heat kernel and Bergman kernel analysis. This new approach of applying techniques coming from analytic geometry is based on the micro-local analysis of the heat kernel and the Bergman kernel in \cite{bouche} and \cite{berman}, respectively, using which we derive sup-norm bounds for cusp forms of integral weight, half-integral weight, and real weight associated to a Fuchsian subgroup of first kind.
Cite
@article{arxiv.1507.00358,
title = {Heat kernels, Bergman kernels, and cusp forms},
author = {Anilatmaja Aryasomayajula},
journal= {arXiv preprint arXiv:1507.00358},
year = {2015}
}
Comments
This article is a slightly elaborate version of the article arXiv:1506.08497, where certain errors have been corrected on this article