乘式丢番图近似的马勒转移定理的一个模拟

IF 0.5 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2023-08-30 DOI:10.1134/S1064562423700680

O. N. German

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引用次数: 0

摘要

Khintchine和Dyson的迁移定理可以很容易地从Mahler的迁移定理中推导出来。在乘法设置中出现了一个障碍，它不允许直接从马勒定理推导出乘法转移定理。还需要考虑一些额外的问题，例如，按量纲进行归纳。本文提出了马勒定理的一个类比，它直接蕴涵了乘法迁移定理。

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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An Analogue of Mahler’s Transference Theorem for Multiplicative Diophantine Approximation

Khintchine’s and Dyson’s transference theorems can be very easily deduced from Mahler’s transference theorem. In the multiplicative setting an obstacle appears, which does not allow deducing the multiplicative transference theorem immediately from Mahler’s theorem. Some extra considerations are required, for instance, induction by the dimension. In this paper we propose an analogue of Mahler’s theorem which implies the multiplicative transference theorem immediately.

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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.