Transcendence of some power series for Liouville number arguments


Caliskan F.

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, cilt.128, sa.3, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 128 Konu: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s12044-018-0407-2
  • Dergi Adı: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES

Özet

In this paper, we prove that some power series with rational coefficients take either values of rational numbers or transcendental numbers for the arguments from the set of Liouville numbers under certain conditions in the field of complex numbers. We then apply this result to an algebraic number field. In addition, we establish the p-adic analogues of these results and show that these results have analogues in the field of p-adic numbers.