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Lagariasí equivalence to the Riemann hypothesis

Tags: harmonic, lagarias, prize, riemann
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Jun11-08, 04:08 AM
P: 23
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
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Jun11-08, 05:31 AM
P: 193
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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