Irrationality criteria for Mahler's numbers (Q1892577)

The paper consists of several criteria concerning the irrationality of numbers \(x= \sum_{n=1}^\infty a_n/ h^n\), where \(0\leq a_n< h\), \(a_1 a_2 a_3 \dots =(g^{n_1})_h (g^{n_2})_h \dots\), \((g^{n_k})_h= c_0 \dots c_{s_k}\) is a finite sequence of digits, \(g^{n_k}= \sum_{j=0}^{s_k} c_j h^j\), \((c_{s_k}\neq 0)\) and the sequence \(\{n_k\}\) is bounded. The proofs use the fact that rational numbers have periodic \(h\)-expansions.