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Heat Kernels, Bergman Kernels, and Cusp Forms

In: Analytic and Algebraic Geometry

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  • Anilatmaja Aryasomayajula

    (IISER Tirupati, Department of Mathematics)

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.

Suggested Citation

  • Anilatmaja Aryasomayajula, 2017. "Heat Kernels, Bergman Kernels, and Cusp Forms," Springer Books, in: Anilatmaja Aryasomayajula & Indranil Biswas & Archana S. Morye & A. J. Parameswaran (ed.), Analytic and Algebraic Geometry, pages 19-28, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-5648-2_2
    DOI: 10.1007/978-981-10-5648-2_2
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