Algebraic independence of certain power series of algebraic numbers

Kumiko Nishioka

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Let f(z) = Σk = 0 zk!. Then in p-adic field we prove that for any algebraic numbers α1,..., αn with 0 < |αi| < 1 (1 ≤ i ≤ n), f(α1),..., f(αn) are algebraically independent over Q if and only if αi αj is not a root of unity for i ≠ j. In the complex field we prove the above result only when n = 2, making use of the p-adic field.

Original languageEnglish
Pages (from-to)354-364
Number of pages11
JournalJournal of Number Theory
Issue number3
Publication statusPublished - 1986 Jul
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory


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