The Riemann zeta in terms of the dilogarithm

We give a representation of the classical Riemann ζ-function in the half plane Res > 0 in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen Gl2-function). We also derive corresponding representations involving the derivatives of the Gl2-function. A generalized symmetrized Müntz-type formula is also derived. For a special choice of test functions it connects to our integral representation of the ζ-function, providing also a computation of a concrete Mellin transform. Certain formulae involving series of zeta functions and gamma functions are also derived.