Abstract
We prove an abstract modularity result for classes of Heegner divisors in the generalized Jacobian of a modular curve associated to a cuspidal modulus. Extending the Gross–Kohnen–Zagier theorem, we prove that the generating series of these classes is a weakly holomorphic modular form of weight . Moreover, we show that any harmonic Maass form of weight defines a functional on the generalized Jacobian. Combining these results, we obtain a unifying framework and new proofs for the Gross–Kohnen–Zagier theorem and Zagier’s modularity of traces of singular moduli, together with new geometric interpretations of the traces with nonpositive index.
Citation
Jan Hendrik Bruinier. Yingkun Li. "Heegner divisors in generalized Jacobians and traces of singular moduli." Algebra Number Theory 10 (6) 1277 - 1300, 2016. https://doi.org/10.2140/ant.2016.10.1277
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