The circle method and diagonal cubic forms

被引：30

作者：

Heath-Brown, DR ^{[1
]}

机构：

[1] Univ Oxford Magdalen Coll, Oxford OX1 4AU, England

来源：

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1998年 / 356卷 / 1738期

关键词：

cubic surface; Hasse-Weil L-function; rational lines; Hardy-Littlewood method; rational points; sum of cubes;

D O I：

10.1098/rsta.1998.0181

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We use the Hardy-Littlewood circle method, in the form developed by Heath-Brown in 1996, to investigate the number of integer zeros of diagonal cubic forms. The results are subject to unproved hypotheses concerning certain Hasse-Weil L-functions. For six variables we show that there are O(P3+epsilon) zeros up to height P, for any epsilon > 0. For four variables we show that there are O(P3/2+epsilon) such zeros, excluding any that lie on rational lines in the corresponding surface.

引用

页码：673 / 699

页数：27

共 15 条

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