二维中伊古萨的一个猜想

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2020-07-14 DOI:10.1353/ajm.2020.0026

James Wright

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引用次数: 5

摘要

我们扩展了Denef、Sperber和Cluckers关于二维环境下Igusa猜想的工作，不再要求多项式对其牛顿图是非简并的。更精确地说，我们为完全指数和建立了清晰一致的界，并为二元的一般拟齐次多项式建立了多项式同余的数目。

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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On a Conjecture of Igusa in Two Dimensions

abstract:We extend work of Denef and Sperber and also Cluckers regarding a conjecture of Igusa in the two dimensional setting by no longer requiring the polynomial to be nondegenerate with respect to its Newton diagram. More precisely we establish sharp, uniform bounds for complete exponential sums and the number of polynomial congruences for general quasi-homogeneous polynomials in two variables.

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.