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This is a Quantitative Study study.

September 22, 2025Open Access

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

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The result establishes a new relationship between Fourier coefficients of cusp forms and class numbers of quadratic forms.
It shows how the summation formula involves the product of four Fourier coefficients of weight 1/2 cusp forms.
The analysis applies to Kohnen's subspace, enhancing understanding of half-integral weight forms.
Involving quadratic forms with integer coefficients, the results may aid in number theory and modular forms research.

Implication

This analysis reveals a spectral summation formula relating Fourier coefficients and class numbers of 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.

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Cite This Study

András Bíró (2025) studied this question.

synapsesocial.com/papers/68d46fdc31b076d99fa6a5e2 https://doi.org/10.48550/arxiv.2507.02522

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Implication

This analysis reveals a spectral summation formula relating Fourier coefficients and class numbers of quadratic forms.

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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