New linear independence measures for values of q-hypergeometric series

On linear independence of values of certain $ q$-series

“…Remark 2. In fact, the inequality n g 0 n 0 + O(1) in condition 3 of Proposition 1 can be replaced by n n 0 + O(l 0 ) (cf., e. g., [3,Section 3]).…”

“…Recently the author [2] proposed a quantitative variant of Bézivin's method; in particular, a weak version of Theorem 1 was proved, with the estimate of the form exp −C 0 m(log H) 2 . A modification of this method was proposed in [3] for the case when the polynomials P (x, y), Q(x) do not depend on x. In this case a much stronger result than Theorem 1 is valid: the estimate for the linear form is polynomial in H and the conditions posed on q can be weakened.…”

“…In this case a much stronger result than Theorem 1 is valid: the estimate for the linear form is polynomial in H and the conditions posed on q can be weakened. In [3] for simplicity…”