Irrationality consequences of rational approximations to zeta values

Determine whether the rational approximations to reciprocals of zeta values and double zeta values constructed from the coefficients C_n^{1;k;1} and C_n^{1;a,b;1} can be improved to yield nontrivial irrationality results for zeta and double zeta values.

Background

The paper constructs infinite families of identities expressing 1/\zeta(k) and 1/\zeta(a,b) as a rational number minus an improper integral whose value tends to zero. Consequently, these identities give nontrivial rational approximations to reciprocals of zeta and double zeta values.

Although the approximations are explicit, the paper does not derive irrationality results from them. The authors leave unresolved whether stronger approximations or related arguments can establish nontrivial irrationality statements.