# Lagarias’ equivalence to the Riemann hypothesis

1. Jun 11, 2008

### CGUE

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. Jun 11, 2008

### mhill

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.