On the global Gross-Prasad conjecture for Yoshida liftings

2002/12/05 by Siegfried Böcherer, Böcherer, Siegfried, Masaaki Furusawa +3
Mathematics · #11F46 #11F67 #22E55 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11F46 #msc:11F67 #msc:22E55

paper · pdf · doi:10.48550/arxiv.math/0212085

29 pages, dedicated to J. Shalika, to appear in the "Shalikafest" supplemental volume to the American Journal of Mathematics

arxiv created 2002/12/05 · arxiv updated 2009/11/30

Abstract

We restrict a Siegel modular cusp form of degree 2 and square free level that is a Yoshida lifting (a lifting from the orthogonal group of a definite quaternion algebra) to the embedded product of two half planes and compute the Petersson product against the product of two elliptic cuspidal Hecke eigenforms. The square of this integral can be explicitly expressed in terms of the central critical value of an L-function attached to the situation. The result is related to a conjecture of Gross and Prasad about restrictions of automorphic representations of special orthogonal groups.

Related

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• Transfer of Siegel cusp forms of degree 2
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