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Metaplectic forms

Metaplectic forms CORRECTIONS TO.. by D. A. KAZHDAN and S. J. PATTERSON (Publications Math6matiques, 59 (I984), 35-I42) Unfortunately the argument on pp. I I9-I20 of this paper were carried out too hastily as was pointed out to us by T. Suzuki. The assertion (X,~, v0, ~) -- o (B r H,,o) is false which necessitates the following additional argument. For v r S for which one * ___ has in I,-- I and (o,,~ [H.,o c~ K, i we have to have for consistency cs,., {,,)(',) x ~,,) (x,~,,, Vo,,, > = Cs(~). ~v ~ H,, v\ Hv By Theorem I. 4. 2 and Proposition I. 2-4 the left-hand side is equal to csu{,,}( ~ X I)(I -- q;*)(I -- q;') ... (I -- q~')/(I- q~-l),. Thus we can define c(~q) ---- lim Cs(~) T(S) st T(S)-- II (z + q~-~)(z + q~-~+ q~-~)... (I + q~-l+ ... + q~-(~-~)). where v~8 I) 4"oo The limit stabilises for large enough S. With this definition the formula of Theorem II. 2.2 should read >. fN -g(n) O(n, fo) dn -- lim Y, e(~) T(S) -~ I-[ ( ),.,~,,, f,. The same modifications should bc made to Theorem II.2.3 and the discussion on p. 13 o. The second author would like to point out that the same applies to the survey << Whittaker Models of Gcncraliscd Thcta Series >> in S/m. TMorie des Nombres de Paris i982-z983, Birkhiiuscr, 1984, pp. 199-232. This applies especially to w 4.7; the correction is already included in w 5.6. The second author is compelled to admit that in this survey he was carried away by a now inexplicable bout of optimism; the conjecture proposed in w 6 cannot be true as stated. Nevertheless it does appear to be true when the functions on either side are restricted to an appropriately small subset of H A as T. Suzuki has kindly informed us. Manuscrit refu le 10 mai 1985. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Publications mathématiques de l'IHÉS Springer Journals

Metaplectic forms

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Publisher
Springer Journals
Copyright
Copyright © 1985 by Publications Mathématiques de L’I.É.E.S.
Subject
Mathematics; Mathematics, general; Algebra; Analysis; Geometry; Number Theory
ISSN
0073-8301
eISSN
1618-1913
DOI
10.1007/BF02698809
Publisher site
See Article on Publisher Site

Abstract

CORRECTIONS TO.. by D. A. KAZHDAN and S. J. PATTERSON (Publications Math6matiques, 59 (I984), 35-I42) Unfortunately the argument on pp. I I9-I20 of this paper were carried out too hastily as was pointed out to us by T. Suzuki. The assertion (X,~, v0, ~) -- o (B r H,,o) is false which necessitates the following additional argument. For v r S for which one * ___ has in I,-- I and (o,,~ [H.,o c~ K, i we have to have for consistency cs,., {,,)(',) x ~,,) (x,~,,, Vo,,, > = Cs(~). ~v ~ H,, v\ Hv By Theorem I. 4. 2 and Proposition I. 2-4 the left-hand side is equal to csu{,,}( ~ X I)(I -- q;*)(I -- q;') ... (I -- q~')/(I- q~-l),. Thus we can define c(~q) ---- lim Cs(~) T(S) st T(S)-- II (z + q~-~)(z + q~-~+ q~-~)... (I + q~-l+ ... + q~-(~-~)). where v~8 I) 4"oo The limit stabilises for large enough S. With this definition the formula of Theorem II. 2.2 should read >. fN -g(n) O(n, fo) dn -- lim Y, e(~) T(S) -~ I-[ ( ),.,~,,, f,. The same modifications should bc made to Theorem II.2.3 and the discussion on p. 13 o. The second author would like to point out that the same applies to the survey << Whittaker Models of Gcncraliscd Thcta Series >> in S/m. TMorie des Nombres de Paris i982-z983, Birkhiiuscr, 1984, pp. 199-232. This applies especially to w 4.7; the correction is already included in w 5.6. The second author is compelled to admit that in this survey he was carried away by a now inexplicable bout of optimism; the conjecture proposed in w 6 cannot be true as stated. Nevertheless it does appear to be true when the functions on either side are restricted to an appropriately small subset of H A as T. Suzuki has kindly informed us. Manuscrit refu le 10 mai 1985.

Journal

Publications mathématiques de l'IHÉS – Springer Journals

Published: Aug 30, 2007

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