On the values of certain q-hypergeometric series II

As a continuation of the previous work by the authors having the same title, we study the arithmetical nature of the values of certain q-hypergeometric series phi(z; q) with a rational or an imaginary quadratic integer q with \q\ > 1, which is related to a g-analogue of the Bessel function J(0)(z). The main result determines the pairs (q, alpha) with alpha is an element of K for which phi(alpha; q) belongs to K, where K is an imaginary quadratic number field including q.