论文标题
$ L $ - 导体的价值$ 32 $
$L$-values for conductor $32$
论文作者
论文摘要
近年来，罗杰斯（Rogers）和祖德林（Zudilin）开发了一种将椭圆曲线附带的$ l $ values编写为时期的方法。为了将此方法应用于更广泛的$ L $值集合，我们研究了Eisenstein系列，并确定其在Cusps的傅立叶系列。随后，我们将指挥32椭圆曲线的$ L $值作为Eisenstein系列的组成部分，并在$ k> 1 $中评估为一个时期。作为综上的结果，我们为$ l（e，k）$的生成功能提供简单的积分表达式，当时（或奇数）$ k $在正整数上运行。
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.
