Heat kernels, Bergman kernels, and cusp forms

Anilatmaja Aryasomayajula

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arXiv · 1507.00358

Heat kernels, Bergman kernels, and cusp forms

Anilatmaja Aryasomayajula

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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.

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Anilatmaja Aryasomayajula. 2015-07-01. Heat kernels, Bergman kernels, and cusp forms. https://arxiv.org/abs/1507.00358

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