The Riemann zeta in terms of the dilogarithm

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We give a representation of the classical Riemann $��$-function in the half plane $\Re s>0$ in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen $Gl_2$-function). We also derive corresponding representations involving the derivatives of the $Gl_2$-function. A generalized symmetrized M��ntz-type formula is also derived. For a special choice of test functions it connects to our integral representation of the $��$-function, providing also a computation of a concrete Mellin transform. Certain formulae involving series of zeta functions and gamma functions are also derived.

revised version, major changes in Sec. 3 and 5, 25 pages

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