The distribution of primitive roots in finite fields

Primitive Roots In Short Intervals

“…have the same upper bound up to an error term. An asymptotic relation for the exponential sums (38) is provided in Lemma 5.1. This result expresses the first exponential sum in (38) as a sum of simpler exponential sum and an error term.…”

“…for any number N ≫ p 1/2+ε , where M ≥ 2 is a fixed number, and ε > 0 is a small number, see [18], [14], [9], [38]. More elaborate exponential sums methods can reduce the size of the interval to N ≫ p 1/4+ε , see [2].…”