Antisymmetry of real quadratic singular moduli
Number Theory
2026-03-11 v1
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.
Keywords
Cite
@article{arxiv.2603.09764,
title = {Antisymmetry of real quadratic singular moduli},
author = {Sören Sprehe},
journal= {arXiv preprint arXiv:2603.09764},
year = {2026}
}