Explicit bounds for small prime nonresidues.

Let χ be a Dirichlet character modulo a prime p. We give explicit upper bounds on q 1 < q 2 < ... < q n , the n smallest prime nonresidues of χ. More precisely, given n 0 and p 0 there exists an absolute constant C = C (n 0 , p 0) > 0 such that q n ≤ C p 1 4 (log ⁡ p) n + 1 2 whenever n ≤ n 0 and p ≥ p 0. [ABSTRACT FROM AUTHOR]