SOME GENERALIZED LACUNARY POWER SERIES WITH ALGEBRAIC COEFFICIENTS FOR MAHLER'S U - NUMBER ARGUMENTS

Kekec G.

TAIWANESE JOURNAL OF MATHEMATICS, vol.18, no.1, pp.1-26, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.11650/tjm.18.2014.2285
  • Journal Name: TAIWANESE JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-26
  • Istanbul University Affiliated: Yes

Abstract

In this work, we show that under certain conditions the values of some generalized lacunary power series with algebraic coefficients for Mahler's U-m-number arguments belong to either a certain algebraic number field or U-i=1 U-i in Mahler's classification of the complex numbers, where t denotes a positive rational integer dependent on the coefficients of the given series and on the argument. Moreover, the obtained results are adapted to the field Q(p) of p-adic numbers.