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.
ASJC Scopus subject areas
- Algebra and Number Theory