On Polyadic Liouville Numbers

The study of polyadic Liouville numbers has begun relatively recently. The canonical expansion of a polyadic number λ is of the form This series converges in any field Q p of p -adic numbers. A polyadic number λ is called a polyadic Liouville number (or a Liouville polyadic number) if for any and P there exists a positive integer A such that for all primes p satisfying the inequality holds. Given a positive integer m , let denote the result of k raised to the power k successively m times. Let , and let Theorem 1 states that, for any positive integer and any prime number p , the series converges to a transcendental element of the ring Z p . In other words, the polyadic number α is globally transcendental.