ARITHMETICAL RESULTS ON CERTAIN q-SERIES, II

Abstract

As in Part I, entire transcendental solutions of certain mth order linear q-difference equations are investigated arithmetically, where now the polynomial coefficients are much more general. The purpose of this paper is to produce again lower bounds for the dimension of the K-vector space generated by 1 and the values of these solutions at m successive powers of q, where K is the rational or an imaginary quadratic field. A new feature in the proof is to use simultaneously positive and negative powers of q as interpolation points leading to an extra parameter in the main result extending its applicability.