Geodesic
An elementary proof of the irrationality of $\zeta(3)$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2009), pp. 28-35

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An elementary proof of the irrationality of $\zeta(3)$ is presented. The proof is based on a two times more dense sequence of diophantine approximations to this number than the sequence in the original proof of Apery. 
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     author = {Yu. V. Nesterenko},
     title = {An elementary proof of the irrationality of $\zeta(3)$},
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     pages = {28--35},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2009_4_a4/}
}
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Yu. V. Nesterenko. An elementary proof of the irrationality of $\zeta(3)$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2009), pp. 28-35. http://geodesic.mathdoc.fr/item/VMUMM_2009_4_a4/