Irrationality Criteria for Mahler′s Numbers Original Research Article

For positive integers m and h ≥ 2, let (m)h denote the finite sequence of digits of m written in h-ary notation. It is known that the real number ah(g) = 0 · (gn1)h(gn2)h(gn3)h… with g ≥ 2, h ≥ 2 is irrational, if the sequence (ni) of non-negative integers is unbounded. We study the case where (ni) is bounded, and prove several irrationality criteria.