# Name of Legendre symbol?

Generally, $(a/p)$ is called "the Legendre symbol" where $p$ is an odd prime, but I don't like this naming since this naming is not formal. That is, this terminology is not designating a specific object.

Does it sound OK to call $(a/p)$ "the Legendre symbol of $a$ mod $p$" or "the Legendre symbol of $a$ over $p$"?

What about naming the function $(-/p):\mathbb{Z}\rightarrow \mathbb{Z}$ "the Legendre symbol mod $p$?

What would be a good terminology to emphasize a subject $a$ or emphasize $(-/p)$ as a function?