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Lagarias’ equivalence to the Riemann hypothesis 
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#1
Jun1108, 04:08 AM

P: 23

Lagarias’ equivalence to the Riemann hypothesis should be discussed, i.e., if
h_{n} := nth harmonic number := 1/1 + 1/2 + · · · + 1/n, and σ_{n} := divisor function of n := sum of positive divisors of n, then if n > 1, h_{n} + e^{hn} ln h_{n} > σ_{n}. There is a $1,000,000 prize for the proof of this at www.claymath.org 


#2
Jun1108, 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 HilbertPolya conjecture or the condition of a Fourier transform having only real zeros. 


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