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Math Help - Help with Riemann's Hypothesis

  1. #16
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    Re: Help with Riemann's Hypothesis

    line break = \cr
    RR
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  2. #17
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    Re: Help with Riemann's Hypothesis

    Quote Originally Posted by robinlrandall View Post
    OK, Then show me a zero from the equation where this is NOT true.
    You are mistakenly thinking that if 0=\sum_{n=0}^{\infty}a_n then a_n must be zero for all n. The terms sum to zero, there is no requirement for any term to be zero.
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  3. #18
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    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
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  4. #19
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    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
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  5. #20
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    Re: Help with Riemann's Hypothesis

    Quote Originally Posted by robinlrandall View Post
    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 n^s=n^{1-s} and you will see that it is false.
    For example, n=2, s=0.4+0.2i leads to 2^{0.4+0.2i}= 1.31+0.182i and 2^{0.6-0.2i}=1.5-0.209i
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