Evaluation of Bianchi Rigid Meromorphic Cocycles at Big ATR Points

2025/11/26 by Lennart Gehrmann, Gehrmann, Lennart, Xavier Guitart +3 · 1 citation
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2511.21171

Abstract

We develop the tools required to effectively evaluate the Bianchi rigid meromorphic cocycles introduced by Darmon-Gehrmann-Lipnowski at big ATR points, and use them to obtain the first numerical verification of the conjectured algebraicity of these special values. Moreover, our computations suggest that these special values exhibit behaviour analogous to that of the special values of Borcherds products on Hilbert modular surfaces at big CM points.

Citations

• Rigid meromorphic cocycles for orthogonal groups
• The values of the Dedekind-Rademacher cocycle at real multiplication points
• A quaternionic construction of p-adic singular moduli

Cited by

• Eisenstein class of a torus bundle and log-rigid analytic classes for SL_n(ℤ)

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