On the global Gross-Prasad conjecture for Yoshida liftings

Details On the global Gross-Prasad conjecture for Yoshida liftings On the global Gross-Prasad conjecture for Yoshida liftings

2002-12-05

arxiv.org/abs/math/0212085v1

Mathematics

Number Theory

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

Scientific paper

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.

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