Math Is Fun Forum

Yeah, I'm okay with this thread staying, especially because of the helpful information that some people have posted about Riemann and complex numbers and stuff, but I feel better now that the revealing material has been deleted. I'm sort of paranoid about someone else stumbling upon my idea and publishing a paper on it before I do.

Anyway, I got my results back for a maths test today. 92%. (I actually thought I'd get 100% but I guess 92% is okay.) My teacher actually made a mistake when marking my test... when you solve a quadratic inequality by means of a parabola you only need the x-intercepts and the sign of a to dermine whether the graph is concave up or down, but she went and wrote in the y-intercept and vertex, as if it was needed heh.

"Okay, I don't really understand it so I'm probably wrong but what se7en claims is that he can prove any true statement but didn't Gödel prove that there are true statements that cannot be proven hence disproving se7en's claim.

Sorry if what I just said was completely wrong but like I said I don't really understand Gödel's Incompleteness Theorem." - John

That's actually very interesting, I'll have to think about that.

Okay, I have two questions about the Riemann hypothesis.

The Riemann hypothesis states that...

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Let a be a complex number such that a is not a negative even number.

If zeta(a) = 0, then Re(a) = 1/2, or rather, the real part of a is 1/2.

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But how can a equal a negative even number? A negative even number is an INTEGER, not a complex number.

The only way I can see that a could be a negative even number is if we have the product of two conjugate complex numbers... but if a = 89 say, what is the real part of a? a would equal (5 + j8)(5 - j8)... there are two real parts.

Here's a guess...

(5 + j8)(5 - j8)
= 25 + j40 - j40 - j^2(64)
= 25 + j^2(64)

So does the real part equal 25 and the imaginary part equal j(64)?

But 89 also equals 90 + j^2

so we could also say that the real part of 89 is 90 and the imaginary part is j.

I guess we could also say that the real part of (5 + j8)(5 - j8) is 5, because both real parts are 5.

So we have three totally different answers that all sound right heh.

I suppose for my proof I could sort of just brute force it out... say that if x = a + jb and the real part of x is 1/2 (a = 1/2) then zeta(x) = 0... even if we are talking about two or more totally different numbers that have real part 1/2. Yeah... that could work.

Okay, now my other question...

The generalized Riemann hypothesis conjectures that neither the Riemann zeta function nor any Dirichlet L-series has a zero with real part larger than 1/2.

But does this mean that for every x such that x is the real part of some imaginary number a, if x is less than 1/2 then there is DEFINITELY a zero? In other words, is it possible, for example, for there to be a zero when the real part equals 1/4 but there's no zero when the real part equals 1/8?

"when do you think your algorithm will be sufficiently used by you so you'd feel comfortable publishing some proofs and thus releasing it to the mathematical community?" - Zhylliolom

I'll go public when I've proved Riemann and I've written out neat copies of my proofs. There are also some programs I want to write first. Basically, I want my thesis to be finished and polished before I go public. Thanks for the information btw.

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