Lagariasí equivalence to the Riemann hypothesis


by CGUE
Tags: harmonic, lagarias, prize, riemann
CGUE
CGUE is offline
#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
Better thermal-imaging lens from waste sulfur
Hackathon team's GoogolPlex gives Siri extra powers
Bright points in Sun's atmosphere mark patterns deep in its interior
mhill
mhill is offline
#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