On the global GrossPrasad conjecture for Yoshida liftings
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 Lfunction attached to the situation. The result is related to a conjecture of Gross and Prasad about restrictions of automorphic representations of special orthogonal groups.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2002
 DOI:
 10.48550/arXiv.math/0212085
 arXiv:
 arXiv:math/0212085
 Bibcode:
 2002math.....12085B
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Representation Theory;
 11F67;
 11F46;
 22E55
 EPrint:
 29 pages, dedicated to J. Shalika, to appear in the "Shalikafest" supplemental volume to the American Journal of Mathematics