One-level densities in families of Gr\"ossencharakters associated to CM
elliptic curves
One-level densities in families of Gr\"ossencharakters associated to CM
elliptic curves
We study the low-lying zeros of a family of $L$-functions attached to the CM elliptic curves $E_d \;:\; y^2 = x^3 - dx$, for each odd and square-free integer $d$. Writing the $L$-function of $E_d$ as $L(s-\frac12, \xi_d)$ for the appropriate Gr\"ossencharakter $\xi_d$ of conductor $\mathfrak{f}_d$, the family $\mathcal F_d$ …