| Автор | HSU, CHIH-HUNG |
| Дата выпуска | 1997 |
| dc.description | A well-known conjecture of E. Artin [1] states that for any integers $a \ne {\pm}1$ and $a$ is not a perfect square, there are infinitely many prime integers $p$ for which $a$ is a primitive root $({\bmod}\, p)$. An analogue of this conjecture for function fields was attacked successfully by Bilharz [2] in 1937 using the Riemann hypothesis for curves over finite fields (subsequently proved by A. Weil). The original conjecture of Artin remains open, though it was shown to be true if one assumes the Generalized Riemann hypothesis by Hooley [7]. In recent years, this conjecture of Artin has also been formulated and studied for elliptic curves over global fields instead of just ${\rm G}_m$ (the original case) (see [11]). |
| Издатель | Cambridge University Press |
| Тема | Kummer–Carlitz extensions |
| Тема | Artinʼs conjecture |
| Название | On Artinʼs conjecture for the Carlitz module |
| DOI | 10.1023/A:1017932203320 |
| Electronic ISSN | 1570-5846 |
| Print ISSN | 0010-437X |
| Журнал | Compositio Mathematica |
| Том | 106 |
| Первая страница | 247 |
| Последняя страница | 266 |
| Аффилиация | HSU CHIH-HUNG; National Taiwan Normal University |
| Выпуск | 3 |
