On Moduli Spaces, Equidistribution, Estimates, and Rational Points of Algebraic Curves
We consider the moduli spaces of hyperelliptic curves, Artin–Schreier coverings, and some other families of curves of this type over fields of characteristic p. By using the Postnikov method, we obtain expressions for the Kloosterman sums. The distribution of angles of the Kloosterman sums was inves...
Збережено в:
| Дата: | 2001 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2001
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4335 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We consider the moduli spaces of hyperelliptic curves, Artin–Schreier coverings, and some other families of curves of this type over fields of characteristic p. By using the Postnikov method, we obtain expressions for the Kloosterman sums. The distribution of angles of the Kloosterman sums was investigated on a computer. For small prime p, we study rational points on curves y 2 = f(x). We consider the problem of the accuracy of estimates of the number of rational points of hyperelliptic curves and the existence of rational points of curves of the indicated type on the moduli spaces of these curves over a prime finite field. |
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