Shifted convolution L-series values for elliptic curves

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 genus(X0(N )) = 1. arXiv:1608.05462v2 [math.NT]

On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras

“…It is immediately clear from the definition that the function Z E has poles precisely where the value of the Eichler integral E E (τ ) lies in the period lattice Λ E . It is an open problem to classify those points τ in the complex upper half-plane H this occurs, but the following lemma, whose proof can be found for example in [2], allows us to rule out poles in the situation where E and the modular curve X 0 (N) are actually isomorphic, so where the degree of φ E is 1. For the purpose of this paper, it is important to consider the behaviour of both the (completed) Weierstrass mock modular form at other cusps than infinity.…”