Heat Kernels, Bergman Kernels, and Cusp Forms

Anilatmaja Aryasomayajula ()
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Anilatmaja Aryasomayajula: IISER Tirupati, Department of Mathematics

A chapter in Analytic and Algebraic Geometry, 2017, pp 19-28 from Springer

Abstract: 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 from [3] and [2], 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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-5648-2_2

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DOI: 10.1007/978-981-10-5648-2_2

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