Antisymmetry of real quadratic singular moduli
S\"oren Sprehe
TL;DR
This paper proves a conjecture about the antisymmetry of real quadratic singular moduli and explores related modularity properties of Kudla-Millson divisors, advancing understanding in number theory and automorphic forms.
Contribution
It confirms Darmon-Vonk's conjecture on antisymmetry and establishes modularity of Kudla-Millson divisors using advanced cocycle analysis.
Findings
Confirmed antisymmetry of real quadratic singular moduli
Proved modularity of a Kudla-Millson divisors generating series
Developed analysis of rigid meromorphic cocycles for split orthogonal groups
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Analytic Number Theory Research