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There are many equivalent statements to the Riemann Hypothesis (RH) and statements that, if true, would imply the RH holds. But F(s) = zeta(2s)/zeta(s) being an
by mathematician23 10y ago
There are many equivalent statements to the Riemann Hypothesis (RH) and statements that, if true, would imply the RH holds. But F(s) = zeta(2s)/zeta(s) being analytic in the critical strip, outside the critical line, DOES NOT imply the RH is true.
That's my point, it doesn't matter if the author really showed F(s) is analytic in that region or not.
Showing something is equivalent to the RH is a major area of research and so is finding statements that directly imply the RH. The function F(s) is very well known and a simple function, so if there were any simple statements involving it that directly implies the RH, we would know by now. I hope this helps.
- vskp2016 10y agoThe paper clearly demonstrates that if F(s) has poles on the critical line, RH is proved.This is because the poles in F(s) correspond to zeros of zeta(s) and it is well known that there are no other zeros outside the critical strip (except for the trivial zeros). The paper has proved that the only poles of F(s),occur on this critical line. Ok bye!