A summation formula for triples of quadratic spaces

Abstract

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 ${\mathcal{Q}}_1,{\mathcal{Q}}_2,{\mathcal{Q}}_3$, respectively. Let \begin{align*} Y \subset \prod_{i=1}V_i \end{align*} be the closed subscheme consisting of $(v_1,v_2,v_3)$ on which ${\mathcal{Q}}_1(v_1)={\mathcal{Q}}_2(v_2)={\mathcal{Q}}_3(v_3)$. 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.

Appendix removed. This paper has been accepted by Advances in Mathematics

References in corpus (4)

• On the formal arc space of a reductive monoid
• Normalized intertwining operators and nilpotent elements in the Langlands dual group
• On a conjecture of Braverman and Kazhdan
• Zeta integrals, Schwartz spaces and local functional equations