Holomorphic Eisenstein series with Jacobian twists
Lev A. Borisov
Abstract
For every point on the Jacobian of the modular curve X0(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 X1(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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