On simultaneous diophantine approximations to ζ(2)ζ(2) and ζ(3)ζ(3)

We present a hypergeometric construction of rational approximations to ζ(2)ζ(2) and ζ(3)ζ(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, ζ(2)ζ(2) and ζ(3)ζ(3) with rational coefficients. We then go further to formalize the arithmetic structure of these specific linear forms by introducing a new notion of (simultaneous) diophantine exponent. Finally, we study the properties of this newer concept and link it to the classical irrationality exponent and its generalizations given recently by S. Fischler.