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...
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| Datum: | 2001 |
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| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4335 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510465467088896 |
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| author | Glazunov, N. M. Глазунов, Н. М. Глазунов, Н. М. |
| author_facet | Glazunov, N. M. Глазунов, Н. М. Глазунов, Н. М. |
| author_sort | Glazunov, N. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:26:49Z |
| description | 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. |
| first_indexed | 2026-03-24T02:57:26Z |
| format | Article |
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| id | umjimathkievua-article-4335 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:57:26Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b5/94ea81b1584d5847c2c353c17a605db5.pdf |
| spelling | umjimathkievua-article-43352020-03-18T20:26:49Z On Moduli Spaces, Equidistribution, Estimates, and Rational Points of Algebraic Curves О пространствах модулей, равнораспределенности, оценках и рациональных точках алгебраических кривых Glazunov, N. M. Глазунов, Н. М. Глазунов, Н. М. 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. Розглядаються простори модулів гіпереліптичних кривих та накриттів Артіна — Шраєра, а також деяких сімей таких кривих над полями характеристики $р$. Методом О. Г. Постнікова отримано вирази для сум Клостермана. Розподіл кутів сум Клостермана досліджено на ЕОМ. Для невеликих простих р досліджено раціональні точки на кривих $у^2 - f(x)$, Розглянуто-проблему точності оцінок числа раціональних точок гіпереліптичних кривих та існування раціональних точок кривих вказаного вигляду на просторах модулів цих кривих над простим скінченним полем. Institute of Mathematics, NAS of Ukraine 2001-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4335 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 9 (2001); 1174-1183 Український математичний журнал; Том 53 № 9 (2001); 1174-1183 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4335/5374 https://umj.imath.kiev.ua/index.php/umj/article/view/4335/5375 Copyright (c) 2001 Glazunov N. M. |
| spellingShingle | Glazunov, N. M. Глазунов, Н. М. Глазунов, Н. М. On Moduli Spaces, Equidistribution, Estimates, and Rational Points of Algebraic Curves |
| title | On Moduli Spaces, Equidistribution, Estimates, and Rational Points of Algebraic Curves |
| title_alt | О пространствах модулей, равнораспределенности, оценках и рациональных точках алгебраических кривых |
| title_full | On Moduli Spaces, Equidistribution, Estimates, and Rational Points of Algebraic Curves |
| title_fullStr | On Moduli Spaces, Equidistribution, Estimates, and Rational Points of Algebraic Curves |
| title_full_unstemmed | On Moduli Spaces, Equidistribution, Estimates, and Rational Points of Algebraic Curves |
| title_short | On Moduli Spaces, Equidistribution, Estimates, and Rational Points of Algebraic Curves |
| title_sort | on moduli spaces, equidistribution, estimates, and rational points of algebraic curves |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4335 |
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