Arithmetic Properties of Some Power Series and Fundamental Units of Certain
Real Quadratic Number Fields
In this study, arithmetic properties of some power series and fundamental units of certain real quadratic fields are investigated. This thesis consists of five chapters.
In the first chapter, a general investigation about the Theory of Transcendental Numbers and the Fundamental Units of Real Quadratic Number Fields is presented.
In the second chapter, main definitions and theorems about Liouville Numbers, Number Fields, Fundamental Units and Continued Fractions are given.
In the third chapter, the methods which we used in order to prove our original teorems are summarized.
In the fourth chapter, firstly it is shown that under certain conditions the values of some power series with rational coefficients for some Liouville number arguments belong to either the field of rational numbers or the set of Liouville numbers. Then, for all real quadratic fields except for Richaud-Degert type such that the period in the continued fraction expansion of the quadratic irrational number is equal to 7, , coefficients of the fundamental unit and the continued fraction expansion of the quadratic irrational number are determined explicitly and the original theorems are obtained.
An evaluation of the results of this study is carried out in the fifth chapter.
OSANÇLIOL Alen
Tez Adı : Ağırlıklı Orlicz Uzaylarının Soyut Harmonik Analizi
Danışman : Prof. Dr. Serap ÖZTOP
Anabilim Dalı : Matematik
Programı : -
Mezuniyet Yılı : 2013
Tez Savunma Jürisi : Prof. Dr. Serap ÖZTOP
Prof. Dr. Nazım SADIK
Prof. Dr. Aydın AYTUNA
Prof. Dr. Yusuf AVCI
Doç. Dr. Erhan ÇALIŞKAN
Dostları ilə paylaş: |
