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This may seem stupid question, but I'm curious about this.

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?

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I think for the Legendre question it should be "a on p". But I could be wrong.

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  • $\begingroup$ I agree with this! :) $\endgroup$ – KCd Jan 3 '15 at 20:26

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