Is there any standard way to read (in English) the Legendre symbol (ap) (http://en.wikipedia.org/wiki/Legendre_symbol), say, similar to "a choose b" which is used for the binomial coefficients?

5$\begingroup$ I wouldn't mind knowing how this is read in other languages, by the way :) $\endgroup$– Mariano SuárezÁlvarezFeb 16, 2010 at 15:02

1$\begingroup$ I am almost certain that the answer to your question is "no", and for everyone that posts an answer saying "well I say it this way" this is in some sense more evidence that the answer really is "no". Isn't that strange? $\endgroup$– Kevin BuzzardFeb 16, 2010 at 15:23

1$\begingroup$ I think Kevin is correct. (As for myself, I say "the Legendre symbol of a with respect to p", because I don't know what else one is suppose to say.) $\endgroup$– EmertonFeb 16, 2010 at 15:34

$\begingroup$ Mariano: In German,(ab) is read "a nach b", according to a German mathematician who asked me the original question. $\endgroup$– Keivan KaraiFeb 16, 2010 at 16:02
3 Answers
I say "a on b" for the Legendre/Jacobi/Kronecker symbol. This works because, as an American, I say "a over b" for an ordinary fraction.

2$\begingroup$ I don't think I have ever heard anyone in English say anything other than "a on p" for (ap) when trying to read the symbol. Perhaps they've said something more involved like "the Legendre symbol with denominator p" for the function (*p). $\endgroup$– KConradFeb 16, 2010 at 21:43

3$\begingroup$ Really? Everyone says "a on p"? I think I usually still just say "a over p" for the Legendre symbol (at the board), sometimes prefaced by "the Legendre symbol." $\endgroup$– KimballJun 15, 2011 at 0:34
I use "a legendre b" for the Legendre symbol. I know this is probably not very common and a bit idiosyncratic but I think it is quite clear.
I recently started using "QR a b"

$\begingroup$ To use this in the statement of quadratic reciprocity, you'd have to talk about QR $p$ $q$ and QR $q$ $p$, which don't sound good to me. (An issue that came up in my thesis: If $\ell$ and $p$ are already taken for primes, and $q$ is already taken for a prime power, what is the notation for anotheer prime?) $\endgroup$– LSpiceJun 14, 2011 at 22:07