改进了超几何函数中有效无理性测度的常数

Q4 Mathematics

Moscow Journal of Combinatorics and Number Theory Pub Date : 2021-11-01 DOI:10.2140/moscow.2022.11.161

P. Voutier

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引用次数: 0

摘要

在本文中，我们简化和改进了有效非理性测度中出现的常数c，|（a/b）m/n−p/q|>c|q|−（κ+1），该常数是从a/b接近1的超几何方法获得的。在我们的结果中，c对|a|的依赖性是最好的（在许多情况下对n的依赖性也是如此）。对于某些应用程序，这个常数对|a|的依赖性变得很重要。我们还为超几何函数建立了一些新的不等式，这些不等式在其他丢番图设置中很有用。

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Improved constants for effective irrationality measures from hypergeometric functions

. In this paper, we simplify and improve the constant, c , that appears in eﬀective irrationality measures, | ( a/b ) m/n − p/q | > c | q | − ( κ +1) , obtained from the hypergeometric method for a/b near 1. The dependence of c on both | a | in our result is best possible (as is the dependence on n in many cases). For some applications, the dependence of this constant on | a | becomes important. We also establish some new inequalities for hypergeometric functions that are useful in other diophantine settings.

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来源期刊

Moscow Journal of Combinatorics and Number Theory Mathematics-Algebra and Number Theory

CiteScore

0.80

自引率

0.00%

发文量