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Holomorphic Eisenstein series with Jacobian twists

Lev A. Borisov
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Abstract

For every point on the Jacobian of the modular curve $X_0(l)$ we define and study certain twisted holomorphic Eisenstein series. These are particular cases of a more general notion of twisted modular forms which correspond to sections on the modular curve $X_1(l)$ of the degree zero twists of line bundles of usual modular forms. We conjecture that a point on the Jacobian is rational if and only if the ratios of these twisted Eisenstein series of the same weights have rational coefficients.

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Lev A. Borisov. 2004-10-27. Holomorphic Eisenstein series with Jacobian twists. https://arxiv.org/abs/math/0410333

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