“…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]).…”
Section: Main Propositionmentioning
confidence: 99%
“…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.…”
mentioning
confidence: 99%
“…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…”
We prove, in a quantitative form, linear independence results for values of a certain class of q -series, which generalize classical q -hypergeometric series. These results refine our recent estimates.
“…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]).…”
Section: Main Propositionmentioning
confidence: 99%
“…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.…”
mentioning
confidence: 99%
“…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…”
We prove, in a quantitative form, linear independence results for values of a certain class of q -series, which generalize classical q -hypergeometric series. These results refine our recent estimates.
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