-values for conductor
arXiv:2008.06749 · doi:10.1016/j.jnt.2021.09.013
Abstract
In recent years, Rogers and Zudilin developed a method to write -values attached to elliptic curves as periods. In order to apply this method to a broader collection of -values, we study Eisenstein series and determine their Fourier series at cusps. Subsequently, we write the -values of an elliptic curve of conductor 32 as an integral of Eisenstein series and evaluate the value at explicitly as a period. As a side result, we give simple integral expressions for the generating functions of when even (or odd) runs over positive integers.
25 pages