Geodesic
Irrationality of the sums of zeta values
Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 607-618

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In this paper, we establish a lower bound for the dimension of the vector spaces spanned over $\mathbb Q$ by 1 and the sums of the values of the Riemann zeta function at even and odd points. As a consequence, we obtain numerical results on the irrationality and linear independence of the sums of zeta values at even and odd points from a given interval of the positive integers. 
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     title = {Irrationality of the sums of zeta values},
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T. G. Hessami Pilehrood; Kh. Hessami Pilehrood. Irrationality of the sums of zeta values. Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 607-618. http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a12/