On special values of spinor L-functions of Siegel cusp eigenforms of genus 3

Francesco Chiera Kirill Vankov 1, *
* Auteur correspondant
Abstract : We compute the special values for the spinor L-function L(s,F12) in the critical strip s={12,...,19}, where F12 is the unique (up to a scalar) Siegel cusp form of degree 3 and weight 12, which was constructed by Miyawaki. These values are proportional to the product of Petersson inner products of Ramanujan's Delta by itself and the cusp form of weight 20 for SL(2,Z) by itself by a rational number and some power of Pi. We also verify this result numerically using Dokchitser's ComputeL PARI package. To our knowledge this is the first example of a spinor L-function of Siegel cusp forms of degree 3, when the special values can be computed explicitly.
Type de document :
Pré-publication, Document de travail
IF_PREPUB. 2008
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https://hal.archives-ouvertes.fr/hal-00823402
Contributeur : Kirill Vankov <>
Soumis le : jeudi 16 mai 2013 - 23:21:51
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

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  • HAL Id : hal-00823402, version 1
  • ARXIV : 0805.2114

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Francesco Chiera, Kirill Vankov. On special values of spinor L-functions of Siegel cusp eigenforms of genus 3. IF_PREPUB. 2008. <hal-00823402>

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