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 [split] Understanding Kneser Riemann method andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 01/13/2016, 06:41 PM (01/13/2016, 05:36 PM)sheldonison Wrote: I'm writing this equations in terms of the slog, since my latest program, fatou.gp calculates the slog. The uniqueness criteria, equivalent to Kneser, is that the upper complex plane theta(z) has a very special property, that as $\Im(z)$ approaches +imag infinity, theta(z) approaches a constant. Since theta(z) is a 1-cyclic function, this tells you that: $\theta(z) = \sum_{n=0}^{\infty} a_n \cdot \exp(2n\pi i z)\; \;$ notice the absence of negative terms as compared with the general 1-cyclic: $\sum_{n=-\infty}^{\infty} a_n \cdot \exp(2n\pi i z)\; \;$ Ok, so this looks a Fourier series with unknown coefficients. How do you compute the coefficients $a_n$? Maybe it's obvious, but I don't know much about Fourier series. « Next Oldest | Next Newest »

 Messages In This Thread [split] Understanding Kneser Riemann method - by andydude - 01/13/2016, 04:01 PM RE: Should tetration be a multivalued function? - by marraco - 01/13/2016, 05:31 PM RE: Should tetration be a multivalued function? - by sheldonison - 01/13/2016, 05:36 PM RE: Should tetration be a multivalued function? - by andydude - 01/13/2016, 06:41 PM RE: Should tetration be a multivalued function? - by andydude - 01/13/2016, 09:21 PM RE: Should tetration be a multivalued function? - by sheldonison - 01/13/2016, 10:55 PM RE: Should tetration be a multivalued function? - by andydude - 01/13/2016, 09:29 PM RE: Should tetration be a multivalued function? - by sheldonison - 01/13/2016, 10:58 PM

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