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Generalized Wiener Ikehara for exp[1/2](n) instead of n ? - Printable Version

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Generalized Wiener Ikehara for exp[1/2](n) instead of n ? - tommy1729 - 12/17/2012

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