Proof (?!) that RH is false?

[bdodson]

Anyone heard anything about this one? Serious (elementary) analytic
number theory, by an Indian mathematician I haven't heard of.

http://arxiv.org/archive/math

then NT --> recent, then march 14 for

Title: The Riemann Hypothesis
Authors: Tribikram Pati

-bd

[Zeta-Flux]

I saw this. As with all preprints (but more especially with ones which claim to answer hard questions) one must wait for the experts to analyze the proof.

It would have been nice if he had computed an explicit bound within which there was a zero off of the line. Glancing through the proof, such a bound doesn't seem unreasonably hard to obtain (although some of the absolute constants involved in the proof may not be constructible).

[davieddy]

How many hours of maths goes down the pan if he's right?

[bdodson]

Originally Posted by davieddy

How many hours of maths goes down the pan if he's right?

Not sure that anyone would imagine the RH going down .... well, there's
that, just to start. But if the unthinkable happened, the Generalized
RH on L-functions and on Dedekind zeta functions would seem to be
in question; which I don't think it is, again, not so much imaginable.

There's also the Clay problem on generalized Peterson, and large
chunks of the rest of automorphic forms. I tried google on zeta
functions and got:

http://secamlocal.ex.ac.uk/people/st...afunctions.htm

How about 45% of math foundations, about what we (most mathematicians)
believe to be true? More, maybe. -bd

[davieddy]

45% of maths foundations.
That sounds incredibly precise.
Wonder what David Hilbert would make of this.

[bdodson]

Originally Posted by davieddy

45% of maths foundations.
That sounds incredibly precise.
Wonder what David Hilbert would make of this.

Uhm; well, it's commonly known that 79.837% of all
statistics are entirely made-up. The usage of "foundations"
isn't the one in the nature/validity of proof, sorry. More
like what we'd like to be able to prove, but then going on from
there to what would be next.

Hilbert is a good point of reference for the first question though.
While he's (very!) well known for his own list of problems (the ones
from the previous millenium), he's supposed to have said that
if he were able to come back after 100 years, and ask one question,
the one he'd want to know was whether RH had been proven yet
(iirc).

I'd be very surprised if the supposed disproof were to actually
supply info on finding a zero off the critical line. Seems much more
likely that there's an error; but there's probably someone here with
expertise in analytic number theory able to offer a more authoritative
view.

-Bruce

[bdodson]

Originally Posted by bdodson

I tried google on zeta functions and got:

http://secamlocal.ex.ac.uk/people/st...afunctions.htm
-bd

I actually tried looking up sci.math.research, and even sci.math, but
they don't seem to have any new info --- two of the posts being from
the person that sent the question to me (of all unlikely people). I even
tried google on RH (something often recommended by posters in this
forum), from which I found another link on (what seems to be) the same
site as above

http://secamlocal.ex.ac.uk/people/st...a/RHproofs.htm

a long page of proofs and/or disproofs of RH. We may not be able to get
an expert opinion unless the evaluation of the argument falls within
his/her job description. (sigh!) -bd