Rational points on complete intersections of cubic and quadric hypersurfaces over F q ( t ) $\mathbb {F}_q(t)$

IF 1 2区数学 Q1 MATHEMATICS Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-24 DOI:10.1112/jlms.12991

Jakob Glas

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引用次数: 0

Abstract

Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over $F_{q} (t)$ , provided $char (F_{q}) > 3$ . Under the same hypotheses, we also verify weak approximation.

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F q ( t ) $\mathbb {F}_q(t)$ 上三次方和二次方超曲面完全交点上的有理点

利用德尔塔法的二维版本，我们建立了维数至少为 23 over F q ( t ) $\mathbb {F}_q(t)$，条件为 char ( F q ) > 3 $\operatorname{char}(\mathbb {F}_q)>3$的立方超曲面和二次超曲面的非奇异完全交点上有界高的有理点数的渐近公式。在同样的假设下，我们也验证了弱逼近。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.