From: Tal Kubo Subject: Re: "what is a reciprocity law?" Date: Tue, 12 Jan 1999 01:25:09 -0500 To: rusin@math.niu.edu Keywords: Proving quadratic reciprocity with Stokes' Theorem If I remember correctly, the harmonic-theory proofs such as in Farkas & Kra's book on Riemann surfaces (Weil recip. for Green's functions of divisors) are based on Stokes theorem. I think some of the proofs based on the tame symbol also use Stokes but in a way essentially equivalent to using the residue theorem. ============================================================================== From: Tal Kubo Subject: Re: "what is a reciprocity law?" Date: Tue, 12 Jan 1999 02:09:41 -0500 (EST) To: Dave Rusin On Tue, 12 Jan 1999, Dave Rusin wrote: > Thanks for the reference; I'll take a look. I don't remember F&K's proof as being too enlightening, though. The electrostatic interpretation -- "force felt at Q from a point charge at P" is symmetric in P and Q -- is nice but I don't know any reference for it. Maybe by tracing through a Greens-function theoretic proof that the height pairing is symmetric one can see if it is related to differential forms in some deeper way (antisymmetry, poincare duality, K_2, ...). > >Date: Tue, 12 Jan 1999 01:25:09 -0500 > ^^^^^ > "Don't tell me not to burn the candle at both ends; > tell me where to get more wax!") :-) "...early in the evening, just about suppertime...". by the way, you mailed earlier about a Diophantine equation, x^2 = 2^y - 7. i saw later that a generalization of it was given in some high school contest, so there must be some elementary solution.