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The 1978 preprint by S.Kato 'On an explicit formula for class-1 Whittaker functions on split reductive groups over p-adic fields' is cited by papers involving unramified computations of local integrals, such as Casselman–Shalika's 'The unramified principal series of p-adic groups. II. The Whittaker function'.

May I know if there is any link containing S.Kato's 1978 preprint?

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  • $\begingroup$ @coLaideronnette Thank you, but the paper you linked is an earlier paper by T.Shintani, not the preprint by S.Kato I am referring to. $\endgroup$
    – L-JS
    Commented Aug 12 at 2:57

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Professor Atsushi Murase from Kyoto Sangyo University was kind enough to reach out to Professor Kato for the 1978 preprint. It's a 41 page typewritten text in English. I am uncertain whether I can post it publicly, but if you write me an email I can forward the preprint I received to you.
[email protected]

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Professor Tomonori Moriyama from Osaka University gave me some background information:

The paper you mentioned is the master thesis of S-I. Kato under the supervision of Prof. N. Iwahori, which is hand-written and written in Japanese. I read it in the library of Graduate School of Mathematical Sciences of University of Tokyo more than 20 years ago.

The basic strategy of proof is more or less the same as T. Shintani's 1976 paper On an explicit formula for class-1 “Whittaker functions” on GL$_n$ over $p$-adic fields, but there are much more complicated case-by-case arguments.

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  • $\begingroup$ Thank you so much, I have reached out to you via email. $\endgroup$
    – L-JS
    Commented Aug 16 at 9:02
  • $\begingroup$ Would you mind if people other than the OP wrote to you for a copy of the preprint? $\endgroup$
    – Aurel
    Commented Aug 19 at 13:54
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    $\begingroup$ certainly not, please go ahead and drop me a line so I can mail it to you. $\endgroup$
    – Carlo Beenakker
    Commented Aug 19 at 13:55

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