Diophantine approximations for a constant related to elliptic functions

Abstract

This paper is devoted to the study of rational approximations of the ratio η(λ)/omega(λ), where omega(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/omega)(λ) with λ∈ \bm{Q} and we shall find new measures of irrationality, both in the archimedean and non archimedean case.