特殊立方零点和对偶变化

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2024-08-14 DOI:10.1112/jlms.12975

Victor Y. Wang

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引用次数: 0

摘要

设 F $F$ 是六变量 Z $\mathbb {Z}$ 上的对角立方形式。从杜克-弗里德兰德-伊瓦尼茨（Duke-Friedlander-Iwaniec）和希斯-布朗（Heath-Brown）的三角法中的对偶变化中，我们无条件地提取了直径为 X → ∞ $X \rightarrow \infty$ 的区域中 F $F$ 的某些特殊积分零点的加权计数。希斯-布朗在四个变量中做了同样的工作，但我们的分析有所不同，并捕捉到了一些新的特征。我们还为更一般的 F $F$ 提出了一个公理框架。

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Special cubic zeros and the dual variety

Let $F$ be a diagonal cubic form over $Z$ in six variables. From the dual variety in the delta method of Duke–Friedlander–Iwaniec and Heath-Brown, we unconditionally extract a weighted count of certain special integral zeros of $F$ in regions of diameter $X \to \infty$ . Heath-Brown did the same in four variables, but our analysis differs and captures some novel features. We also put forth an axiomatic framework for more general $F$ .

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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.