Irrationality of the sums of zeta values

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.