Generalized Wiener Ikehara for exp[1/2](n) instead of n ? - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Generalized Wiener Ikehara for exp[1/2](n) instead of n ? (/showthread.php?tid=766) 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