# 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2013

Littérature citée [12 références]

https://hal.archives-ouvertes.fr/hal-00933967
Contributeur : Simon Dauguet <>
Soumis le : mardi 21 janvier 2014 - 13:50:14
Dernière modification le : jeudi 11 janvier 2018 - 06:12:18

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SimultDioApp.pdf
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### Identifiants

• HAL Id : hal-00933967, version 1
• ARXIV : 1401.5322

### Citation

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

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