Poisson summation for Hankel transforms

TL;DR

This paper extends the Poisson summation formula to Hankel transforms in the context of $L$-embeddings, generalizing classical summation formulas like Voronoi, with implications for number theory and harmonic analysis.

Contribution

It introduces a Poisson summation formula for Hankel transforms associated with $L$-embeddings, expanding the theoretical framework of summation formulas.

Findings

Generalization of Poisson summation for Hankel transforms

Connection to classical Voronoi summation formula

Potential applications in automorphic forms and number theory

Abstract

In this article we study the Poisson summation for Hankel transform in the sense of Braverman-Kazhdan-Ngo in the special case of $L$-embedding $\rho: GL_1\rightarrow GL_2$. We view such a summation formula as the generalization of the classical Voronoi summation formula.