On linear independence measures of the values of Mahler functions

被引：1

作者：

Vaananen, Keijo ^{[1
]}

Wu, Wen ^{[2
]}

机构：

[1] Univ Oulu, Dept Math Sci, POB 3000, Oulu 90014, Finland

[2] South China Univ Technol, Sch Math, Guangzhou 510641, Guangdong, Peoples R China

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2018年 / 148卷 / 06期

基金：

芬兰科学院;

关键词：

linear form; Mahler function; Hermite-Pade approximation; GENERATING-FUNCTIONS; CONTINUED FRACTIONS; SEQUENCE; NUMBERS; APPROXIMATIONS;

D O I：

10.1017/S0308210518000148

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We estimate the linear independence measures for the values of a class of Mahler functions of degrees 1 and 2. For this purpose, we study the determinants of suitable Hermite-Pade approximation polynomials. Based on the non-vanishing property of these determinants, we apply the functional equations to get an infinite sequence of approximations that is used to produce the linear independence measures.

引用

页码：1297 / 1311

页数：15

共 50 条

[31] Linear independence of values of Tschakaloff functions with different parameters
Vaananen, Keijo
Zudilin, Wadim
JOURNAL OF NUMBER THEORY, 2008, 128 (09) : 2549 - 2558
[32] THE LINEAR INDEPENDENCE OF VALUES OF SOME HYPERGEOMETRIC-FUNCTIONS
VASILENKO, ON
VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1985, (05): : 34 - 37
[33] LINEAR INDEPENDENCE OF INTEGER VALUES OF ALGEBRAIC-FUNCTIONS
STUMBO, F
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1992, 6B (04): : 913 - 931
[34] On Linear Independence of Differentiated with Respect to Parameter Functions and Their Values
P. L. Ivankov
Russian Mathematics, 2019, 63 : 22 - 30
[35] ANALYSIS OF MEASURES OF ALGEBRAIC INDEPENDENCE OF VALUES OF E-FUNCTIONS
GORELOV, VA
IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII MATEMATIKA, 1992, (10): : 6 - 11
[36] ESTIMATES OF ALGEBRAIC INDEPENDENCE MEASURES OF VALUES OF E-FUNCTIONS
GORELOV, VA
SIBERIAN MATHEMATICAL JOURNAL, 1990, 31 (05) : 732 - 743
[37] Mahler Measures as Linear Combinations of L-values of Multiple Modular Forms
Samart, Detchat
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2015, 67 (02): : 424 - 449
[38] ALGEBRAIC INDEPENDENCE OF THE VALUES OF CERTAIN SERIES BY MAHLER METHOD
BECKER, PG
MONATSHEFTE FUR MATHEMATIK, 1992, 114 (3-4): : 183 - 198
[39] LINEAR INDEPENDENCE OF VALUES OF THE q-EXPONENTIAL AND RELATED FUNCTIONS
Dixit, Anup B.
Kumar, Veekesh
Pathak, Siddhi S.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2024, 109 (03) : 453 - 463
[40] On the measure of linear and algebraic independence for values of entire hypergeometric functions
Zudilin, VV
MATHEMATICAL NOTES, 1997, 61 (1-2) : 246 - 248

← 1 2 3 4 5 →