Bhargava's composition law and Waldspurger's central value theorem

TL;DR

This paper provides a new proof of Waldspurger's formula connecting toric periods and central L-values of GL2, using distributions on prehomogeneous vector spaces instead of traditional methods.

Contribution

It introduces a novel approach to prove Waldspurger's formula by leveraging distributions on prehomogeneous vector spaces, diverging from previous theta-correspondence and trace formula techniques.

Findings

Reproves Waldspurger's formula using a new method

Establishes a connection between toric periods and L-values

Provides an alternative proof technique for a classical result

Abstract

We reprove a Waldspurger's formula which relates the toric periods and the central values of L-functions of GL2. Our technique, different from the original theta-correspondence approach and the more recent relative trace formula, relies on the exploit of distributions defined on prehomogeneous vector spaces.