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arXiv · 2106.00544

Upper Bound of the Least Quadratic Nonresidues

N. A. Carella
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Abstract

Let $p\geq3$ be a large prime and let $n(p)\geq2$ denotes the least quadratic nonresidue modulo $p$. This note sharpens the standard upper bound of the least quadratic nonresidue from the unconditional upper bound $n(p)\ll p^{1/4\sqrt{e}+\varepsilon}$ to the conjectured upper bound $n(p)\ll (\log p)^{1+\varepsilon}$, where $\varepsilon>0$ is a small number, unconditionally. This improvement breaks the exponential upper bound barrier.

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N. A. Carella. 2021-05-28. Upper Bound of the Least Quadratic Nonresidues. https://arxiv.org/abs/2106.00544

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