The first aim of the talk is to present a compressed version of Campbell-Hausdorff formula in the quotient L/[[L,L],[L,L]]. The second aim is to apply the compressed formula to describe explicitly all Drinfeld associators in the same quotient. Originally, Drinfeld associators appeared in the theory of quasi-Hopf algebras. Formally, an associator is a solution of complicated algebraic equations (pentagon and hexagon) involving 5 and 6 exponentials. The compressed formula is a powerful tool that helps to solve the above exponential equations completely.

In the context of number theory the main result states that the pentagon and hexagon equations do not provide polynomial relations between odd values of the classizal zeta function. The talk is based on the article "Compressed Drinfeld associators" recently published in J. of Algebra 292 (2005), 184-242.