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arXiv · 2602.01473

Theta correspondence and the Borisov-Gunnells relations

Romain Branchereau
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Abstract

We consider a geometric theta correspondence from the first homology of a modular curve, to modular forms of weight $2$. Using Stevens' description of the homology, we find that this map sends modular symbols to product of weight one Eisenstein series, modular caps to weight $2$ Eisenstein series, and hyperbolic cycles to diagonal restrictions of Hilbert-Eisenstein series. We use it to revisit work of Borisov and Gunnells, and explain its connection to a theorem of Li. In particular, we give a geometric proof of certain relations between Eisenstein series.

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Romain Branchereau. 2026-02-01. Theta correspondence and the Borisov-Gunnells relations. https://arxiv.org/abs/2602.01473

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