局部正性和有效丢番图近似

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-11-08 DOI:10.1007/s12188-022-00260-8

Matthias Nickel

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引用次数: 0

摘要

本文提出了一种新的方法来证明丢番图近似的有效结果。这种方法涉及到对除数的局部正性的测量，并结合了Faltings版本的西格尔引理，而不是像戴森引理那样的零估计。然后用它证明了一个关于满足复系数代数方程的两个代数数同时逼近的有效定理。

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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Local positivity and effective Diophantine approximation

In this paper we present a new approach to prove effective results in Diophantine approximation. This approach involves measures of local positivity of divisors combined with Faltings’s version of Siegel’s lemma instead of a zero estimate such as Dyson’s lemma. We then use it to prove an effective theorem on the simultaneous approximation of two algebraic numbers satisfying an algebraic equation with complex coefficients.

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.