A summation formula for triples of quadratic spaces

Let V 1 ,V 2 ,V 3 be a triple of even dimensional vector spaces over a number field F equipped with nondegenerate quadratic forms Q 1 ,Q 2 ,Q 3 , respectively. Let Y⊂∏i=1V i be the closed subscheme consisting of (v 1 ,v 2 ,v 3 ) on which Q 1 (v 1 )=Q 2 (v 2 )=Q 3 (v 3 ). Motivated by conjectures of Braverman and Kazhdan and related work of Lafforgue, Ngô and Sakellaridis we prove an analogue of the Poisson summation formula for certain functions on this space.