Lacunary Power Series and ??-Numbers

AbstractIn this work, the values of certain lacunar power series with rational coefficients for ??-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 ?_?-number,

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