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Old 2007-12-24, 06:58   #1
devarajkandadai's Avatar
May 2004

4748 Posts
Default Another generalised RH?

The Generalised Riemann Hypothesis

Just as 0 is a point of collective convergence for infinitely
many points on the critical line, 1 seems to be a point of collective convergence for many points in the region to the right of 1 on the co-axial plane.

This seems evident from the following program in pari:

Let s= 2 +3*I.

{p(k)=zeta( 2 + 3*I +k*zeta(2+3*I))}

for(k=1,200,print p(k)))

(Incidentally I thank Maxal for giving me preliminary training in programming in pari).

In the above the collective convergence seems to commence from k=

125(approx) onwards.

Needless to say the value of k when collective convergence

commences differs for differenct values of s.

In short, for 0 the critical line is 1/2;for 1, the critical region

is the portion of the axial plane to the right of 1.Are there other

points of collective convergence?

Last fiddled with by devarajkandadai on 2007-12-24 at 07:00
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