Department of
Applied
Mathematics

Recurrence sequences with arithmetic properties

Lutz G. Lucht

Techn. univ. Clausthal

Abstract

Sarkozy (1978) characterized the multiplicative solutions g: N -> C to homogeneous linear recurrence equations with complex coefficients. His intricate proof was extended by Heppner and Maxsein (1985) to multiplicative sequences that are ultimately recurrent. Their result combined with the Polya-Carlson theorem from 1921 explains that power series generated by multiplicative coefficients "in most cases" possess the circle of convergence as natural boundary. Heppner and Maxsein posed the problem to find a simple proof. The talk presents a short proof.