On Artin's conjecture on average and short character sums
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908782790967296 |
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| author | Klurman, Oleksiy Shparlinski, Igor E. Teräväinen, Joni |
| author_facet | Klurman, Oleksiy Shparlinski, Igor E. Teräväinen, Joni |
| contents | Let $N_a(x)$ denote the number of primes up to $x$ for which the integer $a$ is a primitive root. We show that $N_a(x)$ satisfies the asymptotic predicted by Artin's conjecture for almost all $1\le a\le \exp((\log \log x)^2)$. This improves on a result of Stephens (1969). A key ingredient in the proof is a new short character sum estimate over the integers, improving on the range of a result of Garaev (2006). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13355 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Artin's conjecture on average and short character sums Klurman, Oleksiy Shparlinski, Igor E. Teräväinen, Joni Number Theory 11L40, 11N25, 11A07 Let $N_a(x)$ denote the number of primes up to $x$ for which the integer $a$ is a primitive root. We show that $N_a(x)$ satisfies the asymptotic predicted by Artin's conjecture for almost all $1\le a\le \exp((\log \log x)^2)$. This improves on a result of Stephens (1969). A key ingredient in the proof is a new short character sum estimate over the integers, improving on the range of a result of Garaev (2006). |
| title | On Artin's conjecture on average and short character sums |
| topic | Number Theory 11L40, 11N25, 11A07 |
| url | https://arxiv.org/abs/2412.13355 |