Shifted convolution L-series values for elliptic curves

作者：Ali Asra^*; Mani Nitya

来源：ARCHIV DER MATHEMATIK, 2018, 110(3): 225-244.

DOI：10.1007/s00013-017-1112-6

• Elliptic curve
• Modular form
• L-series values
• Holomorphic projection
• Eisenstein series
• Modularity theorem
• Complex multiplication

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 .

• 出版日期2018-3
• 单位MIT