(email received from comet@bayvax.decus.org, 14th January 2004)
Hello,
I looked at http://www.maths.ex.ac.uk/~mwatkins/zeta/RHproofs.htm and glanced
over C. Pradas, "Proof of the Riemann Hypothesis - preliminary notes" and it
appears to me that there is a flaw in the proof.
It is apparent to me that the non-trivial zeros of the Riemann zeta function
on the critical line come in pairs; one with positive "i" and one with negative
"i". (And any zeros in the critical strip, but off the line, would in addition
come in pairs, one on each side of the critical line.)
C. Prada's proof uses a complex conjugate of the Riemann zeta function--he
doesn't indicate that this is necessarily and equivalent for these zeros...
and so I think his proof falls apart around the following line:
"Since zeta(s) is an injection on C, there are no other different real parts of
s, with the same imaginary absolute value |Im(s)| <> 0..."
What do you think?