Notes on the Distribution of Roots Modulo Primes of a Polynomial IV

Abstract

Abstract For polynomials f (x),g 1(x),g 2(x)over ℤ, we report several observations about the density of primes p for which f (x) is fully splitting at p and { g 1 ( r ) p } < { g 2 ( r ) p } \left\{ {{{{g_1}\left( r \right)} \over p}} \right\} < \left\{ {{{{g_2}\left( r \right)} \over p}} \right\} for some root r of f (x) ≡ 0 mod p.