On quadratic approximation for hyperquadratic continued fractions

被引：2
作者：
Ayadi, Khalil [1 ]
Ooto, Tomohiro [2 ]
机构：
[1] Univ Sfax, Fac Sci, Dept Math, Sfax, Tunisia
[2] Tecnos Data Sci Engn Inc, Shinjuku Ku, 27F Tokyo Opera City,340-2 Nishishinjuku, Tokyo 1631427, Japan
来源：
JOURNAL OF NUMBER THEORY | 2020年 / 215卷
关键词：
Diophantine approximation; Positive characteristic; DIOPHANTINE APPROXIMATION; POWER-SERIES; LAURENT SERIES; EXPONENTS; SYMMETRIES;
D O I：
10.1016/j.jnt.2020.02.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study quadratic approximations for two families of hyperquadratic continued fractions in the field of Laurent series over a finite field. As the first application, we give the answer to a question of the second author concerning Diophantine exponents for algebraic Laurent series. As the second application, we determine the degrees of these families in particular case. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页码：171 / 185
页数：15
相关论文
共 17 条
[1]   CONTINUED FRACTIONS OF ALGEBRAIC POWER-SERIES IN CHARACTERISTIC-2 [J].
BAUM, LE ;
SWEET, MM .
ANNALS OF MATHEMATICS, 1976, 103 (03) :593-610
[2]  
Bugeaud Y, 2004, Cambridge Tracts in Mathematics, V160
[3]  
de Mathan B., 1970, Mem. Soc. Math. Fr., V21
[4]   APPROXIMATION EXPONENTS FOR ALGEBRAIC-FUNCTIONS IN POSITIVE CHARACTERISTIC [J].
DEMATHAN, B .
ACTA ARITHMETICA, 1992, 60 (04) :359-370
[5]   Rational approximations to algebraic Laurent series with coefficients in a finite field [J].
Firicel, Alina .
ACTA ARITHMETICA, 2013, 157 (04) :297-322
[6]   Algebraic and badly approximable power series over a finite field [J].
Lasjaunias, A ;
Ruch, JJ .
FINITE FIELDS AND THEIR APPLICATIONS, 2002, 8 (01) :91-107
[7]  
Lasjaunias A., ARXIV170408959
[8]   A note on hyperquadratic continued fractions in characteristic 2 with partial quotients of degree 1 [J].
Lasjaunias, Alain .
ACTA ARITHMETICA, 2017, 178 (03) :249-256
[9]   ON A THEOREM OF LIOUVILLE IN FIELDS OF POSITIVE CHARACTERISTIC [J].
MAHLER, K .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1949, 1 (04) :397-400
[10]   CONTINUED FRACTIONS FOR CERTAIN ALGEBRAIC POWER-SERIES [J].
MILLS, WH ;
ROBBINS, DP .
JOURNAL OF NUMBER THEORY, 1986, 23 (03) :388-404
12