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October, 2001 Diophantine approximations for a constant related to elliptic functions
J. Math. Soc. Japan 53(4): 957-974 (October, 2001). DOI: 10.2969/jmsj/05340957


This paper is devoted to the study of rational approximations of the ratio η(λ)/ω(λ), where ω(λ) and η(λ) are the real period and real quasi-period, respectively, of the elliptic curve y2=x(x-1)(x-λ). Using monodromy principle for hypergeometric function in the logarithm case we obtain rational approximations of (η/ω)(λ) with λQ and we shall find new measures of irrationality, both in the archimedean and non archimedean case.


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Marc HUTTNER. Tapani MATALA-AHO. "Diophantine approximations for a constant related to elliptic functions." J. Math. Soc. Japan 53 (4) 957 - 974, October, 2001.


Published: October, 2001
First available in Project Euclid: 29 May 2008

zbMATH: 1069.11031
MathSciNet: MR1852891
Digital Object Identifier: 10.2969/jmsj/05340957

Primary: 11J61 , 11J82 , 33C75 , 34A20

Keywords: $p$-adic , Differential equations in the complex domain , elliptic integrals , hypergeometric function , Measure of irrationality

Rights: Copyright © 2001 Mathematical Society of Japan

Vol.53 • No. 4 • October, 2001
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