Cusp forms of weight 1/2 and pairs of quadratic forms

TL;DR

This paper establishes a spectral summation formula linking Fourier coefficients of half-integral weight cusp forms to generalized class numbers of quadratic form pairs, advancing understanding in automorphic forms and quadratic forms.

Contribution

It introduces a novel spectral summation formula connecting Fourier coefficients of weight 1/2 cusp forms with class numbers of quadratic form pairs.

Findings

Spectral summation formula derived for Fourier coefficients.

Connection established between cusp forms and quadratic form class numbers.

Provides tools for further research in automorphic forms and quadratic forms.

Abstract

We prove a spectral summation formula for the product of four Fourier coefficients of half-integral weight cusp forms in Kohnen's subspace. The other side of the formula involves certain generalized class numbers of pairs of quadratic forms with integer coefficients.