Lacunary Power Series and 𝑼𝒎-Numbers

Year 2019, Volume: 15 Issue: 4, 365 - 370, 30.12.2019

Fatma Çalışkan

https://doi.org/10.18466/cbayarfbe.622670

Abstract

Abstract

In this work, the values of certain lacunar power series with rational coefficients for 𝑈𝒎-number arguments were determined to be either in a particular algebraic number field or in the set of transcendental numbers under specific circumstances in the complex numbers field. The result was also applied on some of the lacunary power series with coefficients in an algebraic number field. Roth's theorem which is the essential result in Diophantine approximation to algebraic numbers was used to reach the present results.

Keywords

Algebraic number field, power series, transcendental number, 𝑈_𝑚-number

Supporting Institution

Scientific Research Projects Coordination Unit of Istanbul University

Project Number

27422

Thanks

I sincerely thank to Prof. Dr. Bedriye M. ZEREN for important suggestions on this manuscript. This work was supported by Scientific Research Projects Coordination Unit of Istanbul University (project number 27422).

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