Timeline for Weil reciprocity vs Artin reciprocity

7 events

when toggle format	what		by	license	comment
Apr 13, 2014 at 4:48	vote	accept	Kiu
May 8, 2012 at 17:03	history	edited	Dustin Clausen	CC BY-SA 3.0	added 135 characters in body; deleted 135 characters in body
May 8, 2012 at 16:05	comment	added	David E Speyer		It is also worth noting that, if $b \| p-1$, then Artin reciprocity for $K[t]/(t^b-f)$ can be expressed in terms of the Weil symbol as well: the relation is $(f,g)_x^{(p-1)/b} = \mathrm{Art}(L_f/K)_x(g)$. In particular, if $p$ is odd, $b$ is $2$, $g$ is irreducible and $x_1$, ..., $x_n \in X$ are the zeros of $g$, then the product $\prod_{x_i} (f,g)_{x_i}^{(p-1)/b}$ is "take $f$ modulo $g$ and raise it to the $(p^{\deg g}-1)/2$ power", an expression which should be familiar from proofs of quadratic reciprocity.
May 8, 2012 at 16:00	comment	added	Dustin Clausen		OK Chandan, I fancied it up. I also corrected some p's to q's.
May 8, 2012 at 15:59	history	edited	Dustin Clausen	CC BY-SA 3.0	added 109 characters in body
May 8, 2012 at 15:31	comment	added	Chandan Singh Dalawat		Could you insert a few \$s (by which I don't mean American money but the symbol \$) to make your answer more easily readable ?
May 8, 2012 at 15:13	history	answered	Dustin Clausen	CC BY-SA 3.0