M. Murty

A non-abelian large sieve and Artin's primitive root conjecture

A well-known conjecture of Artin states that if $a$ is an integer not equal to $0, \pm 1$ or a perfect square, then there exist infinitely many primes $p$ such that $a$ is a primitive root $(\text{ mod } p)$. In this article, we study a generalization of the classical (abelian) large sieve inequality in non-abelian set...