Register to reply

Lagariasí equivalence to the Riemann hypothesis

by CGUE
Tags: harmonic, lagarias, prize, riemann
Share this thread:
CGUE
#1
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 www.claymath.org
Phys.Org News Partner Science news on Phys.org
Fungus deadly to AIDS patients found to grow on trees
Canola genome sequence reveals evolutionary 'love triangle'
Scientists uncover clues to role of magnetism in iron-based superconductors
mhill
#2
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.


Register to reply

Related Discussions
The Riemann Hypothesis Linear & Abstract Algebra 37
On Riemann Hypothesis Linear & Abstract Algebra 9
Riemann Hypothesis Calculus 9
Riemann Hypothesis General Math 4
Riemann Hypothesis General Math 6