  We show that the logarithm $\log_q$ of the Frobenius morphism $x\to x^q$ is
given by the formula $x\to x\log x$ (the natural logarithm). In particular, it
does not depend on $q$. This is the explicit (although heuristical) formula for
the operator conjectured by Hilbert whose eigenvalues coincide with the zeroes
of the zeta function.
