论文标题
$ l $ l $ unction在循环范围内某些Hecke字符的函数
Nonvanishing of $L$-function of some Hecke characters on cyclotomic fields
论文作者
论文摘要
在本文中，我们显示了在循环范围内的某些Hecke字符的不变。本文的主要成分是对本本函数的计算以及在某些素数（包括高于$ 2 $）的一些素数中的Weil代表作用。作为一个应用程序，我们表明，对于$ p $ - th fermat曲线的雅各布的每个同等因素，其中$ 2 $是二次残留模量$ p $，有许多无限的曲折的分析等级为零。同样，对于$ 11 $ Then Cyclotomic磁场上的一定椭圆形曲线，其雅各布具有复杂的乘法，因此有许多无限的曲折的分析等级为零。
In this paper, we show the nonvanishing of some Hecke characters on cyclotomic fields. The main ingredient of this paper is a computation of eigenfunctions and the action of Weil representation at some primes including the primes above $2$. As an application, we show that for each isogeny factor of the Jacobian of the $p$-th Fermat curve where $2$ is a quadratic residue modulo $p$, there are infinitely many twists whose analytic rank is zero. Also, for a certain hyperelliptic curve over the $11$-th cyclotomic field whose Jacobian has complex multiplication, there are infinitely many twists whose analytic rank is zero.
