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This article is available for purchase or by subscription. See below.
Abstract
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We simplify and improve the constant
that appears in effective irrationality measures,
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obtained from the hypergeometric method for
near
. The
dependence of
on
in our result is best possible (as is the dependence on
in
many cases). For some applications, the dependence of this constant on
becomes important. We also establish some new inequalities for hypergeometric
functions that are useful in other diophantine settings.
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Keywords
diophantine approximation, effective irrationality
measures, hypergeometric functions
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Mathematical Subject Classification
Primary: 11J82, 11J68, 33C05
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Milestones
Received: 31 October 2021
Revised: 18 May 2022
Accepted: 1 June 2022
Published: 13 August 2022
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