Can anyone point me to a reference which talks about periods of elliptic curves and the Poincaré Residue Theorem, hopefully one which uses this residue theorem to explicitly write out the period?
Poincaré Residue Theorem
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elliptic-curves
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1I couldn't find any mention of the Poincare Residue Theorem at Math Reviews, and no helpful mention searching the web generally. What exactly is the PRT? A websearch for "periods of elliptic curves" did turn up several references, but I didn't check them to see whether the period was explicitly written out, nor whether Poincare and/or residues were mentioned. – 2011-06-21
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I am not sure what the Poincaré residue theorem has to do with it, but if you want to read about periods of elliptic curves and to see some integrals worked out explicitly, then have a look at Knapp's book on Elliptic Curves, Chapter XI on Eichler-Shimura theory. In any case, it is a very nice and clear chapter with things that are missing from most other expositions on elliptic curves.