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The Riemann Hypothesis and Fermat's Last Theorem
fahdaldаpy2002
Posted: Submitted by fahdaldаpy2002 on 26 July 2009 - 8:40pm.
Joined: 2008-06-22
Posts: 29
Greetings,
I am posting to notify you all that I have found a brilliant new line of attack on the famous Riemann Hypothesis that I do believe will result in a spectacular proof. This is all my own work and in fact I've been thinking about it for a few years now (I have started working on the problem in 2002), although I have made a crucial breakthrough a short time ago. This proof is the most amazing thing I've ever thought of, extremely simple and elegant. And it works like this:
As is well known from the Riemann zeta function's functional equation, any point in the zeta-set of non-trivial zeros gives rise to at most three others by reflections in the critical line and real axis.
Now, if a certain zero is a counterexample to the Riemann Hypothesis, this gives rise to three other distinct reflected points.
The elliptic curve through the three other points defines an elliptic curve over the rationals. This elliptic curve is clearly not modular. Here is a diagram depicting the situation:
This contradicts the Tagakawa-Shigora conjecture, which states that any elliptic curve over the rationals is modular.
We can therefore conclude that the dimension of the zeta-set is one and thus that the Riemann Hypothesis is true.
I will gladly answer any questions you may have. The method extends to a wealth of other important problems, such as Fermat's Last Theorem, the Goldbach conjecture, n-body problem, continuum hypothesis, etc.