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14 votes
3 answers
3k views

Quadratic reciprocity and Weil reciprocity theorem

I was told that Weil reciprocity theorem (one has two meromorphic function $f,g$ on a complex curve $C$, so $\prod\limits_{x\in C} g(x)^{ord_xf}=\prod\limits_{x\in C}f(x)^{ord_xg} \ $ where $ord_xf$ ...
1 vote
1 answer
260 views

Conceptual explanation for extra/missing $p$ solutions to $x^2+y^2=a \pmod p$ at $a=0$

Throughout, $p$ will denote a prime integer, and $k$ an arbitrary integer. I have worked through V. Lebesgue's proof of quadratic reciprocity outlined by Keith Conrad in this MO thread, and I feel ...