Effective irrationality measures for certain algebraic numbers
نویسندگان
چکیده
منابع مشابه
Effective Irrationality Measures for Certain Algebraic Numbers
A result of Chudnovsky concerning rational approximation to certain algebraic numbers is reworked to provide a quantitative result in which all constants are explicitly given. More particularly, Padé approximants to the function (1 jc)1/3 are employed to show, for certain integers a and b, that |(a/fc) p/q\> cq~* when q > 0. Here, c and k are given as functions of a and b only. In 1964 Baker [1...
متن کاملIdeal Constructions and Irrationality Measures of Roots of Algebraic Numbers
This paper addresses the problem of determining the best results one can expect using the Thue-Siegel method as developed by Bombieri in his equivariant approach to effective irrationality measures to roots of high order of algebraic numbers, in the non-archimedean setting. As an application, we show that this method, under a nonvanishing assumption for the auxiliary polynomial which replaces t...
متن کاملIRRATIONALITY MEASURES FOR CERTAIN q-MATHEMATICAL CONSTANTS
We prove sharp irrationality measures for a q-analogue ofπ and related q-series, and indicate open problems on linear and algebraic independence of the series that might be viewed as q-analogues of some classical mathematical constants.
متن کاملIrrationality measures for some automatic real numbers
This paper is devoted to the rational approximation of automatic real numbers, that is, real numbers whose expansion in an integer base can be generated by a finite automaton. We derive upper bounds for the irrationality exponent of famous automatic real numbers associated with the Thue–Morse, Rudin–Shapiro, paperfolding and Baum–Sweet sequences. These upper bounds arise from the construction o...
متن کاملIrrationality of certain infinite series
In this paper a new direct proof for the irrationality of Euler's number e = ∞ k=0 1 k! is presented. Furthermore, formulas for the base b digits are given which, however, are not computably effective. Finally we generalize our method and give a simple criterium for some fast converging series representing irrational numbers.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1986
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1986-0829632-4