[split] Understanding Kneser Riemann method

[andydude]

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.