Transcendence of some power series for Liouville number arguments

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Atıf İçin Kopyala

Caliskan F.

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, cilt.128, sa.3, 2018 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 128 Sayı: 3
• Basım Tarihi: 2018
• Doi Numarası: 10.1007/s12044-018-0407-2
• Dergi Adı: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Anahtar Kelimeler: Mahler and Koksma classification, Liouville number, algebraic number field, p-adic number
• İstanbul Üniversitesi Adresli: Evet

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.