03/20/2021, 12:34 AM
Ok so apart from the comment of James, I think there is another reason why the gamma trick does not work.
The thing is on the real line -G(-s) gives large negative values for large negative s as desired.
However - G(- k s ) for complex s with large negative part and increasing k gives arg that are neither positive or negative.
Or they give positive values when we want negative ones.
If it even converges.
This makes even the convergeance of A_k(s) problematic for almost every nonreal s and every k. Let alone a limiting k to oo.
And this implies that many functions fail.
But maybe the problem is not so much with the s but with the way we use k.
using k s might be a bad idea because that kinda makes s and k similar in contribution.
Im thinking about new ways to use k.
regards
tommy1729
The thing is on the real line -G(-s) gives large negative values for large negative s as desired.
However - G(- k s ) for complex s with large negative part and increasing k gives arg that are neither positive or negative.
Or they give positive values when we want negative ones.
If it even converges.
This makes even the convergeance of A_k(s) problematic for almost every nonreal s and every k. Let alone a limiting k to oo.
And this implies that many functions fail.
But maybe the problem is not so much with the s but with the way we use k.
using k s might be a bad idea because that kinda makes s and k similar in contribution.
Im thinking about new ways to use k.
regards
tommy1729
