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Apr 27, 2012 at 7:24 comment added Sebastian I am sorry, I should have said: It is not that difficult, especially one does not need much theory. You make a Fourier expansion $f(z)=\Sum_{n\in\mathbb Z^g}a_n \exp^{2\pi i<n,z>}$ and than you use the 'periodicity' in the $B_l$ direction to show that all $a_n$ are determined by $a_0.$
Apr 27, 2012 at 7:18 comment added Alexander Chervov The last sentence " but one can easily show, that there is only one such function up to multiplication by a constant, the famous theta function of J", does not make me happy. How to "easily see" ?
Apr 27, 2012 at 7:12 history answered Sebastian CC BY-SA 3.0