Regarding the preprint by Han and Han: This seems
to have changed in the meantime; the title of the
preprint that the link points to is currently
"Study on the Hilbert's Eighth Problem" (sic),
not "A proof of the Riemann Hypothesis" as given
on your page. The equation numbers also appear to
have changed; the equation that Loreno Heer's
comment refers to as equation 14 seems to be the
one now numbered (2.1.2). I disagree with Loreno's
comment; the application of l'Hôpital's rule would
be allowed here because rho is assumed to be a
k-th order zero and the derivatives of zeta (1-rho)
are taken to be equal in magnitude to the derivatives
of zeta (rho), i.e. to have the same zeros. If this
were the case, it would be permissible to apply
l'Hôpital's rule using the k-th derivatives, since
all previous derivatives would be zero.
However, there is an error in the proof that the
magnitudes of the derivatives are equal (Lemma 3).
The application of the chain rule in equation
(1.3.2) is invalid. (Applying the chain rule in
this manner, one could prove that the derivatives
of any function are equal to its derivatives at
an arbitrary different point.)