Upper Bound of the Least Quadratic Nonresidues
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911199945293824 |
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| author | Carella, N. A. |
| author_facet | Carella, N. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_00544 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Upper Bound of the Least Quadratic Nonresidues Carella, N. A. General Mathematics 2020: Primary 11A15, Secondary 11L40 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. |
| title | Upper Bound of the Least Quadratic Nonresidues |
| topic | General Mathematics 2020: Primary 11A15, Secondary 11L40 |
| url | https://arxiv.org/abs/2106.00544 |