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

Key Points

• 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.