GENERALIZED CONTINUED FRACTION EXPANSIONS WITH CONSTANT PARTIAL DENOMINATORS

We study generalized continued fraction expansions of the form a(1)/N + a(2)/N + a(3)/N +..., where N is a fixed positive integer and the partial numerators alpha(i) are positive integers for all i. We call these expansions dn(N) expansions and show that every positive real number has infinitely many dn(N) expansions for each N. In particular, we study the dn(N) expansions of rational numbers and quadratic irrationals. Finally, we show that every positive real number has, for each N, a dn(N) expansion with bounded partial numerators.