Transcendence of some power series for Liouville number arguments
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, vol.128, no.3, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 128 Issue: 3
- Publication Date: 2018
- Doi Number: 10.1007/s12044-018-0407-2
- Journal Name: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Keywords: Mahler and Koksma classification, Liouville number, algebraic number field, p-adic number
- Istanbul University Affiliated: Yes
Abstract
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.