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I want to find reference of Waldspurger's paper referred at "Sur les coefficients de Fourier des formes modulaires de poids demi-entier" J. Math. Pures Appl. (9) 60 (1981), no. 4, 375–484 (available here at J. Voight's web page).

The name of ref. is [W] J.L Waldspurger, Correspondance de Shimura (J. Math. pures et appl., n 60, 1980, p.1-132).

Is there anyone who has the latter ref.?

I don't know the definition of Hecke algebra of metaplectic group $\mathrm{SL}(2,A)\times\{1,-1\}$.

There are many senses of Hecke algebra but I don't know in the context of that paper ("Sur les coefficients de Fourier des formes modulaires de poids demi-entier" )

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  • $\begingroup$ I don't understand the question or the answers here. Which paper are you looking for? I have Waldspurger's 1980 Correspondance de Shimura paper. The journal reference is as stated in the question, but it doesn't list any of Waldspurger's other papers in the references. $\endgroup$
    – Kimball
    Commented Oct 4, 2020 at 0:12
  • $\begingroup$ I need the paper 1980 correspondance de Shimura . It is ref. Of sur les coefficients de fourier des formes modulaires de poids demi-entier. Thanks :) $\endgroup$
    – MF_cat
    Commented Oct 4, 2020 at 0:31
  • $\begingroup$ Okay, I think you want to ask this question: mathoverflow.net/q/16354/6518 substituting the Shimura correspondence paper for the Fourier coefficient paper. Or do you just want to know the definition of the Hecke algebra? I don't know of an electronic copy online, but you could request a scan from a university library. $\endgroup$
    – Kimball
    Commented Oct 4, 2020 at 0:51
  • $\begingroup$ Yes my question is that. And i want to know the definition and several properties about double covering of sl2(adele) case. Because in the paper (Fourier coefficients paper) the term ‘Hecke algebra’ is used without definition and where is come from. I searched that but there are many different definition. I don’t know which one he want to express. $\endgroup$
    – MF_cat
    Commented Oct 4, 2020 at 1:03

2 Answers 2

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The full reference is

Jean-Loup Waldspurger, "Sur les coefficients de Fourier des formes modulaires de poids demi-entier", (French) Journal de Mathématiques Pures et Appliquées, IX Séries, 60, 375-484 (1981), MR0646366, Zbl 0431.10015.

The paper seems to have not been digitized yet.

Edit following the comment: all the collections of the "Journal de Mathématiques Pures et Appliquées" from the year 1946 to the year 1997 seem to have not been officially digitized yet. The paper "Correspondances de Shimura" by J.-L. Waldspurger makes no exception and possibly, the best you can find is the 1983 summary for the 1983 ICM in Warsaw already pointed out by @CarloBeenakker.

Further edit following the comments. The paper searched seems to be the following one:

Jean-Loup Waldspurger, "Correspondances de Shimura et Shintani" (French), Journal de Mathématiques Pures et Appliquées, IX Séries, 59, 1-132 (1980), MR0577010, Zbl 0412.10019.

In order to get a copy of that paper (which, as already stated, does not seem to be digitized yet) you can try the "old good way" (obviously enhanced by the use of modern technologies), i.e. ask a librarian near you for a copy of it, possibly by doing the following steps

  1. Check for libraries near you holding collections of the journal, in particular the full 1980 year: the Worldcat gives 852 libraries around the world holding collections of this journal, so I expect this will be a relatively easy task.
  2. Chose one library near you which offers the document delivery service: sometimes this service has a fee (that may be significant for long documents, as in this case) but it is not always so, therefore check also if the library is able to make a free copy for you.
  3. Provide them the full reference as stated above, and wait for the copy.
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  • $\begingroup$ Thanks to your answer! But maybe i make some misunderstand. i need the another paper's pdf or scan. thanks you sir, if you have that paper, please introduced the cite $\endgroup$
    – MF_cat
    Commented Oct 3, 2020 at 14:37
  • $\begingroup$ @MF_cat: What part of "This paper is not available in electronic form" do you not understand? What do you think mathematicians did 25 years ago when they needed a paper? $\endgroup$
    – Alexander Woo
    Commented Oct 3, 2020 at 16:01
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    $\begingroup$ @AlexanderWoo --- please tone down; this comment by MF_cat (who is evidently not a native English speaker) referred to a confusing first version of their post, where it seemed as if they requested the 1981 paper, whereas they were looking for a reference to a 1980 paper in the 1981 paper. $\endgroup$
    – Carlo Beenakker
    Commented Oct 3, 2020 at 20:08
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Here is Sur les coefficients de Fourier des formes modulaires de poids demi-entier
and here is Correspondances de Shimura (not the 1980 paper, but a summary of that paper from 1983)

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  • $\begingroup$ Thanks to your answer! But maybe i make some misunderstand. i need the another paper's pdf or scan. thanks you sir, if you have that paper, please introduced the cite $\endgroup$
    – MF_cat
    Commented Oct 3, 2020 at 14:36

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