$L$values for conductor $32$
Abstract
In recent years, Rogers and Zudilin developed a method to write $L$values attached to elliptic curves as periods. In order to apply this method to a broader collection of $L$values, we study Eisenstein series and determine their Fourier series at cusps. Subsequently, we write the $L$values of an elliptic curve of conductor 32 as an integral of Eisenstein series and evaluate the value at $k>1$ explicitly as a period. As a side result, we give simple integral expressions for the generating functions of $L(E,k)$ when even (or odd) $k$ runs over positive integers.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 arXiv:
 arXiv:2008.06749
 Bibcode:
 2020arXiv200806749M
 Keywords:

 Mathematics  Number Theory;
 11F67;
 (Primary) 11F03;
 11F20;
 14H52;
 33E05 (Secondary)
 EPrint:
 25 pages