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

flag	asked Feb 16 2010 at 14:11 Keivan Karai 2,504●8●23

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I wouldn't mind knowing how this is read in other languages, by the way :) – Mariano Suárez-Alvarez Feb 16 2010 at 15:02

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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? – Kevin Buzzard Feb 16 2010 at 15:23

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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.) – Emerton Feb 16 2010 at 15:34

Mariano: In German,(a|b) is read "a nach b", according to a German mathematician who asked me the original question. – Keivan Karai Feb 16 2010 at 16:02

Pete L. Clark · Accepted Answer · 2010-02-16 14:15:26Z UTC

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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.

answered Feb 16 2010 at 14:15

Pete L. Clark
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Thank you for the quick answer! – Keivan Karai Feb 16 2010 at 14:27

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

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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." – Kimball Jun 15 2011 at 0:34

Ken Levasseur · Answer 2 · 2011-06-14 21:19:17Z UTC

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I recently started using "QR a b"

answered Jun 14 2011 at 21:19

Ken Levasseur
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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?) – L Spice Jun 14 2011 at 22:07

Grétar Amazeen · Answer 3 · 2010-02-16 15:00:25Z UTC

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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.

answered Feb 16 2010 at 15:00

Grétar Amazeen
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Is there a standard way to read the Legendre symbol?

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