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Full Version: Generalized Wiener Ikehara for exp[1/2](n) instead of n ?
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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 ...