Open AccessTranscendental continued β-fraction with quadratic pisot basis over Fq((x-1))
Author(s) -
Marwa Gouadri,
M. Hbaib
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1914585g
Subject(s) - mathematics , transcendental number , formal power series , fraction (chemistry) , quadratic equation , field (mathematics) , power series , pure mathematics , element (criminal law) , series (stratigraphy) , discrete mathematics , combinatorics , mathematical analysis , law , geometry , paleontology , chemistry , organic chemistry , political science , biology
Let Fq be a finite field and Fq((x-1)) is the field of formal power series with coefficients in Fq. Let ??Fq((x-1)) be a quadratic Pisot series with deg(?) = 2. We establish a transcendence criterion depending on the continued ?-fraction of one element of Fq((x-1)).