Antisymmetry of real quadratic singular moduli

Sören Sprehe

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arXiv · 2603.09764

Antisymmetry of real quadratic singular moduli

Sören Sprehe

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Abstract

We confirm a conjecture of Darmon-Vonk on the antisymmetry of real quadratic singular moduli. The proof relies on a careful analysis of rigid meromorphic cocycles \`a la Darmon-Gehrmann-Lipnowski for the split orthogonal group on four variables. Moreover, we prove the modularity of a generating series of Kudla-Millson divisors in the spirit of Gross-Kohnen-Zagier.

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Sören Sprehe. 2026-03-10. Antisymmetry of real quadratic singular moduli. https://arxiv.org/abs/2603.09764

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