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


Kekec G.

TAIWANESE JOURNAL OF MATHEMATICS, cilt.18, ss.1-26, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 18 Konu: 1
  • Basım Tarihi: 2014
  • Doi Numarası: 10.11650/tjm.18.2014.2285
  • Dergi Adı: TAIWANESE JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.1-26

Özet

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.