# Help with Riemann's Hypothesis

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• Jun 15th 2014, 12:25 PM
robinlrandall
Re: Help with Riemann's Hypothesis
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RR
• Jun 15th 2014, 12:44 PM
Shakarri
Re: Help with Riemann's Hypothesis
Quote:

Originally Posted by robinlrandall
OK, Then show me a zero from the equation where this is NOT true.

You are mistakenly thinking that if $\displaystyle 0=\sum_{n=0}^{\infty}a_n$ then $\displaystyle a_n$ must be zero for all n. The terms sum to zero, there is no requirement for any term to be zero.
• Jun 15th 2014, 12:58 PM
robinlrandall
Re: Help with Riemann's Hypothesis
Of course all Riemann Hypothesis constraints are in place:
0 < s < 1 the "critical strip"
Am I forgetting any other "normal" R.H. assumptions?
Robin
• Jun 15th 2014, 01:48 PM
robinlrandall
Re: Help with Riemann's Hypothesis
infty
So I'm saying what if I have 0 = Sum 0 x an
n=1
therefore every element is 0
Then if that means s=1/2 and it checks out they are true zeroes
and "an" are constants for all n "as defined by the equation", where are there
any more zeroes to be found? Maybe there's y1 - y123456 = 0 buried somewhere in the equation but I don't see it yet. I'm still looking. Let's see:
(n^(3/4) - n^(1/4))/n - (m^(3/4) - m^(1/4))/m + ... = 0
Yes, I have some work to do. But I chipping away.
Robin
• Jun 16th 2014, 12:26 AM
Shakarri
Re: Help with Riemann's Hypothesis
Quote:

Originally Posted by robinlrandall
infty
So I'm saying what if I have 0 = Sum 0 x an

But you don't have 0 x an, you have bn x an. You are assuming that bn is equal to zero and it doesn't matter if that assumption leads to RH being true, it is still an assumption.

Just take a simple example to test $\displaystyle n^s=n^{1-s}$ and you will see that it is false.
For example, n=2, s=0.4+0.2i leads to $\displaystyle 2^{0.4+0.2i}= 1.31+0.182i$ and $\displaystyle 2^{0.6-0.2i}=1.5-0.209i$
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