On some power series with algebraic coefficients and Liouville numbers

Gül Karadeniz Gözeri

doi:10.1186/1029-242x-2013-178

Abstract

In this work, we consider some power series with algebraic coefficients from a certain algebraic number field K of degree m and investigate transcendence of the values of the given series for some Liouville number arguments.

Highlights

The theory of transcendental numbers has a long history and was originated back to Liouville in his famous paper [ ] in which he produced the first explicit examples of transcendental numbers at a time where their existence was not yet known
The theory of transcendental numbers is closely related to the study of Diophantine approximation
The first classification of this kind was outlined by Maillet in [ ], and others were described by Perna in [ ] and MorduchaiBoltovskoj [ ] but to Mahler’s classification attaches by for the most interest

Summary

Introduction

The theory of transcendental numbers has a long history and was originated back to Liouville in his famous paper [ ] in which he produced the first explicit examples of transcendental numbers at a time where their existence was not yet known. It follows from this that almost all real numbers are transcendental. Let α be an arbitrary algebraic number.

Results

Conclusion