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

2025/07/03 by Biró, András
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.02522

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.

Citations

• Local square mean in the hyperbolic circle problem
• A symplectic restriction problem
• Geometric invariants for real quadratic fields
• Kloosterman sums and Maass cusp forms of half integral weight for the\n modular group
• Heegner points, cycles and Maass forms

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