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arXiv · 2511.21171

Evaluation of Bianchi Rigid Meromorphic Cocycles at Big ATR Points

Lennart Gehrmann·Xavier Guitart·Marc Masdeu
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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.

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Lennart Gehrmann, Xavier Guitart, Marc Masdeu. 2025-11-26. Evaluation of Bianchi Rigid Meromorphic Cocycles at Big ATR Points. https://arxiv.org/abs/2511.21171

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