Shifted convolution L-series values for elliptic curves
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13_2017_1112_ReferencePDF.pdf
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Author(s)
Ali, Asra
Mani, Nitya
Date Issued
January 6, 2018
Publisher
Springer International Publishing
Version
Author's final manuscript
Abstract
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
.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00013-017-1112-6
