论文标题
在有限场上的椭圆形曲线和有效函数的乘法依赖性图像的元素上
On elements of large order of elliptic curves and multiplicative dependent images of rational functions over finite fields
论文作者
论文摘要
令$ e_1 $和$ e_2 $是带有整数参数的legendre表单的椭圆曲线。我们显示存在一个常数的$ c $，因此对于几乎所有素数，除最多$ c $ c $ c $ c $ c $ c $ e_1 \ times e_2 $ e_2 $ modulo $ p $具有等于$ x $协调的时，至少有一个$ p_1 $和$ p_2 $有一个大集团订单。我们还显示出与元素有限磁场相似的丰度
Let $E_1$ and $E_2$ be elliptic curves in Legendre form with integer parameters. We show there exists a constant $C$ such that for almost all primes, for all but at most $C$ pairs of points on the reduction of $E_1 \times E_2$ modulo $p$ having equal $x$ coordinate, at least one among $P_1$ and $P_2$ has a large group order. We also show similar abundance over finite fields of elements whose images under the reduction modulo $p$ of a finite set of rational functions have large multiplicative orders
