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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?

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I wouldn't mind knowing how this is read in other languages, by the way :) –  Mariano Suárez-Alvarez Feb 16 '10 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 '10 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 '10 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 '10 at 16:02
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3 Answers 3

up vote 13 down vote accepted

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.

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Thank you for the quick answer! –  Keivan Karai Feb 16 '10 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 '10 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 '11 at 0:34
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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.

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I recently started using "QR a b"

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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 '11 at 22:07
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