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Lagarias’ equivalence to the Riemann hypothesis

  1. Jun 11, 2008 #1
    Lagarias’ equivalence to the Riemann hypothesis should be discussed, i.e., if
    hn := n-th harmonic number := 1/1 + 1/2 + · · · + 1/n, and
    σn := divisor function of n := sum of positive divisors of n, then if n > 1,
    hn + ehn ln hn > σn.

    There is a $1,000,000 prize for the proof of this at www.claymath.org
  2. jcsd
  3. Jun 11, 2008 #2
    For me this approach is a bit of nonsense, since you can not evaluate the divisor function for every n=0,1,2,3,4,............... not even an asymptotic formula (with a good remainder) is known for divisor function

    I think that the most promising approach will come from Hilbert-Polya conjecture or the condition of a Fourier transform having only real zeros.
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