English

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.

Keywords

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

R2 v1 2026-06-22T10:04:03.165Z