On Simultaneous Approximation of Algebraic Power Series over a Finite Field

On Simultaneous Approximation of Algebraic Power Series over a Finite Field

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 algebraic irrationals. As no analogue of Roth’s theorem for algebraic irrational power series over a finite field...

Full description

Saved in:
Bibliographic Details
Published in:P-adic numbers, ultrametric analysis, and applications Vol. 16; no. 3; pp. 289 - 294
Main Authors: Ayadi, Khalil, Ben Bechir, Chiheb, Elkadri, Samir
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01-09-2024
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Algebra
Mathematics
Mathematics and Statistics
simultaneous approximation
formal power series
continued fraction
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 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 elements.
ISSN:2070-0466
2070-0474
DOI:10.1134/S2070046624030063