On the irrationality of a certain multivariate infinite product

Original Articles

On the irrationality of a certain multivariate infinite product

Published in: Quaestiones Mathematicae
Volume 29 , issue 3 , 2006 , pages: 351–365
DOI: 10.2989/16073600609486169
Author(s): Ping Zhou
Keywords: IRRATIONALITY , RATIONAL APPROXIMATION
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Abstract

By using simultaneous rational approximation, we prove that If q, m, M are integers with q > 1, m ≥ 2, M ≥ m 2 − 2, and r 1, r 2, …, r m are any positive rationals, then at least one of the infinite products
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