Primes with small primitive roots
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909338244743168 |
|---|---|
| author | Ford, Kevin Gabdullin, Mikhail R. Granville, Andrew |
| author_facet | Ford, Kevin Gabdullin, Mikhail R. Granville, Andrew |
| contents | Let $δ(p)$ tend to zero arbitrarily slowly as $p\to\infty$. We exhibit an explicit set $\mathcal{S}$ of primes $p$, defined in terms of simple functions of the prime factors of $p-1$, for which the least primitive root of $p$ is $\le p^{1/4-δ(p)}$ for all $p\in \mathcal{S}$, where $\#\{p\leq x: p\in \mathcal{S}\} \sim π(x)$ as $x\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04649 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Primes with small primitive roots Ford, Kevin Gabdullin, Mikhail R. Granville, Andrew Number Theory 11A07, 11A15, 11A41 Let $δ(p)$ tend to zero arbitrarily slowly as $p\to\infty$. We exhibit an explicit set $\mathcal{S}$ of primes $p$, defined in terms of simple functions of the prime factors of $p-1$, for which the least primitive root of $p$ is $\le p^{1/4-δ(p)}$ for all $p\in \mathcal{S}$, where $\#\{p\leq x: p\in \mathcal{S}\} \sim π(x)$ as $x\to\infty$. |
| title | Primes with small primitive roots |
| topic | Number Theory 11A07, 11A15, 11A41 |
| url | https://arxiv.org/abs/2410.04649 |