Quantitative linear independence of an infinite product and its derivatives

Bundschuh Peter; Vaananen Keijo

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Quantitative linear independence of an infinite product and its derivatives

机译：无限积及其导数的定量线性独立性

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We establish measures for the rational linear independence of 1 and the values of the product Pi(n>0) (1 + z/(q(n) + q(-n))) and its derivatives at finitely many rational points, q not equal 0, +/- 1 being a fixed integer. This is a quantitative improvement upon Bezivin's very recent result in this journal. In contrast to his procedure, we use the method of Pade approximations of the second kind to get the above-mentioned improvement, some generalizations, and several irrationality measures.

机译：我们建立了在有限个有理点q上有理线性独立性1和乘积Pi（n> 0）（1 + z /（q（n）+ q（-n）））及其导数值的度量不等于0，+ /-1是固定整数。这是对贝济文在本刊中的最新结果的定量改进。与他的过程相反，我们使用第二种Pade逼近方法来获得上述改进，一些推广和一些非理性度量。

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来源
《Manuscripta mathematica》 |2009年第4期|共14页
作者
Bundschuh Peter; Vaananen Keijo;
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原文格式 PDF
正文语种 eng
中图分类 510E0056;
关键词
measures; approximations; improvement;

机译：措施;近似值;改进;

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Quantitative linear independence of an infinite product and its derivatives

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