2026/02/01 by Romain Branchereau
Mathematics · #math.NT
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.