Shifted convolution L-series values for elliptic curves
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Abstract
Using explicit constructions of the Weierstrass mock modular form and Eisenstein series coefficients, we obtain closed formulas for the generating functions of values of shifted convolution L-functions associated to certain elliptic curves. These identities provide a surprising relation between weight 2 newforms and shifted convolution L-values when the underlying elliptic curve has modular degree 1 with conductor N such that
$$\text {genus}(X_0(N)) = 1$$
genus
(
X
0
(
N
)
)
=
1
.
Date issued
2018-01-06Department
Massachusetts Institute of Technology. Department of Mathematics; Massachusetts Institute of Technology. Department of MathematicsPublisher
Springer International Publishing