If I say, $f|_{k}$, what does that mean?

Question

If I say, $f|_{k}$, what does that mean? Sorry to be short on words but I can not find it anywhere on google so maybe someone could explain it and what we typically use it for. I ran into the notation in a book and they do not explain what it is.

In what book did you run into this notation? – awllower Oct 22 '14 at 00:47 — awllower, Oct 22 '14 at 00:47

score 2 · Accepted Answer · answered Oct 22 '14 at 00:37

2

It means that if $f$ is defined on the set $X$, and $k \subseteq X$, then $f|_k$ is $f$ restricted to the set $k$.

answered Oct 22 '14 at 00:37

user141592

6,118

score 0 · Answer 2 · answered Oct 22 '14 at 00:46

It might also have the meaning that $f$ is a modular form, and $k\in\operatorname{SL}_2(\mathbb Z),$ and $f\mid_k$ is $f$ under the action of $k.$
Compared to the answer of @Johanna, this shows that, if the context is missing, the meaning of this symbol is not fixed at all.
Hope this helps.

If I say, $f|_{k}$, what does that mean?

2 Answers2