Sur la conjecture de Zagier pour n=4. II

Abstract

We express a general multiple polylogarithm of weight n as an explicit linear combination of multiple polylogarithms of weight n in n-2 variables. We express a general multiple polylogarithm of weight 4 as an explicit linear combination of multiple polylogarithms of type (3,1). We deduce a 4 parameters functional equation expressing a certain linear combination of multiple polylogarithms of type (3,1) as a linear combination of polylogarithms of weight 4.