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Kernels of L-functions of cusp forms

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Abstract

We give a new expression for the inner product of two kernel functions associated to a cusp form. Among other applications, it yields an extension of a formula of Kohnen and Zagier, and another proof of Manin’s Periods Theorem. Cohen’s representation of these kernels as series is also generalized.

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Authors and Affiliations

  1. Department of Mathematics, University of Nottingham, Nottingham, UK

    Nikolaos Diamantis

  2. Department of Mathematics and Computer Science, Bronx Community College, CP 315, 2155 University Avenue, Bronx, NY, 10453, USA

    Cormac O’Sullivan

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  1. Nikolaos Diamantis
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  2. Cormac O’Sullivan
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Correspondence to Cormac O’Sullivan.

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Diamantis, N., O’Sullivan, C. Kernels of L-functions of cusp forms. Math. Ann. 346, 897–929 (2010). https://doi.org/10.1007/s00208-009-0419-4

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  • DOI: https://doi.org/10.1007/s00208-009-0419-4

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