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Preprints, Working Papers, ... Year : 2013

On simultaneous diophantine approximations to $\zeta(2)$ and $\zeta(3)$

Abstract

The authors present a hypergeometric construction of rational approximations to $\zeta(2)$ and $\zeta(3)$ which allows one to demonstrate simultaneously the irrationality of each of the zeta values, as well as to estimate from below certain linear forms in 1, $\zeta(2)$ and $\zeta(3)$ with rational coefficients. A new notion of (simultaneous) diophantine exponent is introduced to formalise the arithmetic structure of these specific linear forms. Finally, the properties of this newer concept are studied and linked to the classical irrationality exponent and its generalisations given recently by S.Fischler.
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Dates and versions

hal-00933967 , version 1 (21-01-2014)

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Simon Dauguet, Wadim Zudilin. On simultaneous diophantine approximations to $\zeta(2)$ and $\zeta(3)$. 2013. ⟨hal-00933967⟩
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