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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$\mathbf{C}^{2}$-saddle method and Beukers' integral


Author: Masayoshi Hata
Journal: Trans. Amer. Math. Soc. 352 (2000), 4557-4583
MSC (2000): Primary 11J82; Secondary 30E99
Published electronically: June 8, 2000
MathSciNet review: 1641099
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Abstract:

We give good non-quadraticity measures for the values of logarithm at specific rational points by modifying Beukers' double integral. The two-dimensional version of the saddle method, which we call $\mathbf{C}^{2}$-saddle method, is applied.


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Additional Information

Masayoshi Hata
Affiliation: Division of Mathematics, Faculty of Integrated Human Studies, Kyoto University, Kyoto 606-8501, Japan
Email: hata@i.h.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02432-6
PII: S 0002-9947(00)02432-6
Keywords: Saddle method, simultaneous approximation, non-quadraticity measure
Received by editor(s): July 14, 1997
Received by editor(s) in revised form: August 26, 1998
Published electronically: June 8, 2000
Article copyright: © Copyright 2000 American Mathematical Society