This is probably an easy question for the experts:

Given two rational functions $f$, $g$ on a non-singular projective algebraic curve X (over an algebraically closed field $k$) and $p \in X$, one defines the Weil symbol $(f, g)_p$ as the value of $(-1)^{ab} f^a g^{-b}$ at $p$ where $a = v_p(g)$ and $b = v_p(f)$. (Here $v_p$ means order of zero/pole at $p$.)

Weil reciprocity claims that product of $(f, g)_p$ for all $p \in X$ is equal to $1$.

My question is whether the Weil symbol can be realized as a special case of the Artin symbol (for an extension of fields of rational functions)?

(Note that the ground field $k$ is not assumed to be of positive characteristic.)

finitefields. But there is version of Weil reciprocity for the latter, and your question would still make sense. $\endgroup$1more comment