Upper Bound of the Least Quadratic Nonresidues

2021/05/28 by Carella, N. A.
#2020: Primary 11A15 #FOS: Mathematics #General Mathematics (math.GM) #Secondary 11L40

paper · doi:10.48550/arxiv.2106.00544

Abstract

Let p≥3 be a large prime and let n(p)≥2 denotes the least quadratic nonresidue modulo p. This note sharpens the standard upper bound of the least quadratic nonresidue from the unconditional upper bound n(p)≪ p^1/4√(e)+ε to the conjectured upper bound n(p)≪ (log p)^1+ε, where ε>0 is a small number, unconditionally. This improvement breaks the exponential upper bound barrier.

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