On Simultaneous Approximation of Algebraic Power Series over a Finite Field

IF 0.5 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI:10.1134/s2070046624030063

Khalil Ayadi, Chiheb Ben Bechir, Samir Elkadri

引用次数: 0

Abstract

In 1970, W. M. Schmidt [6] generalized Roth’s well-known theorem on rational approximation to a single algebraic irrational, to include simultaneous rational approximation for a given \(n\) algebraic irrationals. As no analogue of Roth’s theorem for algebraic irrational power series over a finite field exists, we will show that there is no analogue of Schmidt’s theorem for such \(n\) elements.

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论有限域上代数幂级数的同时逼近

摘要 1970年，W. M. Schmidt[6]将Roth著名的关于单个代数无理数的有理逼近定理推广到包括给定的（n）个代数无理数的同时有理逼近。由于有限域上代数无理幂级数的 Roth 定理不存在类似的定理，我们将证明对于这样的 \(n\) 元素，Schmidt 定理也不存在类似的定理。

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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来源期刊

P-Adic Numbers Ultrametric Analysis and Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： This is a new international interdisciplinary journal which contains original articles, short communications, and reviews on progress in various areas of pure and applied mathematics related with p-adic, adelic and ultrametric methods, including: mathematical physics, quantum theory, string theory, cosmology, nanoscience, life sciences; mathematical analysis, number theory, algebraic geometry, non-Archimedean and non-commutative geometry, theory of finite fields and rings, representation theory, functional analysis and graph theory; classical and quantum information, computer science, cryptography, image analysis, cognitive models, neural networks and bioinformatics; complex systems, dynamical systems, stochastic processes, hierarchy structures, modeling, control theory, economics and sociology; mesoscopic and nano systems, disordered and chaotic systems, spin glasses, macromolecules, molecular dynamics, biopolymers, genomics and biology; and other related fields.