The Generalization of the Pinkerle Theorem for the K-term Recurrence Equations

V. I. Parusnikov


Abstract: In 1894 Pinkerle proved the theorem, which assist the connection between the existence of the so-called minimal solutions of a system of recurrence relations and the convergence of related continued fraction. In this paper we consider solutions of the infinite system of the (k+1)-term recurrence relations q_n =_{_j=1}∑^{^k-1} p_k-j,nq_n-j , p_1,n ≠ 0, n = 0,1, … , with coefficients p in a field F. The connection between such recurrence relations and (k-2)-dimensional continued fractions is stated. The analogy of the Pinkerle theorem is proved.