Using the norm
valid for any , , consider the case of , and multiplying (1) over all primes p, define a real function of two variables:
where is the Riemann Zeta function.
For , the right-hand product of (2) converges absolutely and in that range one can equate:
Apply the Laplacian on each side of (3):
The right-hand side of (4) converges absolutely for without claims as to the convergence of (3) in the same range. Thus the left-hand side of (4) exists, is finite and always negative for all
which precludes the existence of zeroes of Zeta to the right of the critical line(?)
Can anyone spot an obvious flaw? I have been twisting it in my head for quite a while before posting but can't seem to see what is wrong except it is too simple...The last step in (4) was checked with Mathematica online and is pretty straightforward. Thanks.