科研之友
微信
新浪微博
Facebook
分享链接
摘要
Given a multiplicative subgroup and , assuming the Generalized Riemann Hypothesis, we determine an asymptotic formula for the number of primes p a parts per thousand currency sign x for which ind (p) I%26quot; = m, where ind (p) I%26quot; = (p - 1)/|I%26quot; (p) | and I%26quot; (p) is the reduction of I%26quot; modulo p. This problem is a generalization of some earlier works by Cangelmi-Pappalardi, Lenstra, Moree, Murata, Wagstaff, and probably others. We prove, on GRH, that the primes with this property have a density and, in the case when I%26quot; contains only positive numbers, we give an explicit expression for it in terms of an Euler product. We conclude with some numerical computations.
- 出版日期2013-10
