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Critical values of L-functions on GSp 2 × Gl 2

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Abstract

This paper deals with Deligne's conjecture on the critical values of L-functions. Let Z G ⊗ h (s) denote the tensor product L-function attached to a Siegel modular form G of weight k and an elliptic cusp form h of weight l. We assume that the first Fourier-Jacobi coefficient of G is not identically zero. Then Deligne's conjecture is fully proven for Z G ⊗ h (s), when l≤2k−2 and partly for the remaining case.

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Authors and Affiliations

  1. Kunzenhof 4B, 79117, Freiburg, Germany

    Siegfried Böcherer

  2. Max-Planck Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Bernhard E. Heim

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  1. Siegfried Böcherer
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  2. Bernhard E. Heim
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Correspondence to Bernhard E. Heim.

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Supported by the von Neumann Fund at the Institute for Advanced Study, Princeton

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Böcherer, S., Heim, B. Critical values of L-functions on GSp 2 × Gl 2 . Math. Z. 254, 485–503 (2006). https://doi.org/10.1007/s00209-005-0945-z

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