On the second smallest prime non-residue

2010/11/19 by Kevin J. McGown, McGown, Kevin J.
Mathematics · #11A15 #11N25 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A15 #msc:11N25

paper · pdf · doi:10.48550/arxiv.1011.4492

arxiv created 2010/11/19 · arxiv updated 2010/11/22

Abstract

Let χ be a non-principal Dirichlet character modulo a prime p. Let q₁<q₂ denote the two smallest prime non-residues of χ. We give explicit upper bounds on q₂ that improve upon all known results. We also provide a good upper estimate on the product q₁ q₂ which has an upcoming application to the study of norm-Euclidean Galois fields.

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