Tetration Forum

Full Version: Generalized Wiener Ikehara for exp[1/2](n) instead of n ?
You're currently viewing a stripped down version of our content. View the full version with proper formatting.
Is there a Generalized Wiener Ikehara theorem for exp[1/2](n) instead of n ?

While considering Dirichlet series I wonder what would happen if we take a(0) + a(1)/exp[1/2](1)^s + a(2)/exp[1/2](2)^s + ... + a(n)/exp[1/2](n)^s instead of a(0) + a(1)/1^s + a(2)/2^s + ... a(n)/n^s.

Since exp^[1/2](n) grows faster than any polynomial P(n) we cannot apply the normal Wiener Ikehara theorem in most cases.

Im hoping to 'bridge' analytic number theory and tetration in this way ...

regards

tommy1729