A character sum for root system
Author:
Ronald Evans
Journal:
Proc. Amer. Math. Soc. 114 (1992), 627635
MSC:
Primary 11L05; Secondary 11T24, 17B20, 17B25, 33C80
MathSciNet review:
1073525
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Abstract: A character sum analog of the MacdonaldMorris constant term identity for the root system is proved. The proof is based on recent evaluations of Selberg character sums and on a character sum analog of Dixon's summation formula. A conjectural evaluation is presented for a related sum.
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197–209 (1982). MR 659148
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, The evaluation of Selberg character sums, Enseign. Math. (to appear).
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Math. Soc. 3 (1988), no. 1, 111–128. MR 975841
(90e:11120)
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𝐺₂, SIAM J. Math. Anal. 19 (1988),
no. 6, 1462–1474. MR 965267
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18 (1987), no. 3, 880–883. MR 883574
(88f:05017), http://dx.doi.org/10.1137/0518065
 [1]
 G. W. Anderson, The evaluation of Selberg sums, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), 469472. MR 1076474 (91m:11109)
 [2]
 R. J. Evans, Identities for products of Gauss sums over finite fields, Enseign. Math. (2) 27 (1981), 197209. MR 659148 (83i:10050)
 [3]
 , Character sum analogues of constant term identities for root systems, Israel J. Math. 46 (1983), 189196. MR 733348 (85c:11073)
 [4]
 , The evaluation of Selberg character sums, Enseign. Math. (to appear).
 [5]
 R. J. Evans and W. A. Root, Conjectures for Selberg character sums, J. Ramanujan Math. Soc. 3 (1988), 111128. MR 975841 (90e:11120)
 [6]
 F. G. Garvan, A beta integral associated with the root system , SIAM J. Math. Anal. 19 (1988), 14621474. MR 965267 (89k:33002)
 [7]
 J. Greene, The Bailey transform over finite fields (to appear).
 [8]
 K. Ireland and M. Rosen, A classical introduction to modern number theory, Graduate Texts in Math., vol. 84, SpringerVerlag, New York, 1982. MR 661047 (83g:12001)
 [9]
 I. G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal. 13 (1982), 9881007. MR 674768 (84h:17006a)
 [10]
 W. G. Morris, Constant term identities for finite and affine root systems, Ph.D. thesis, Univ. of Wisconsin, Madison, 1982.
 [11]
 D. Zeilberger, A proof of the case of Macdonald's root systemDyson conjecture, SIAM J. Math. Anal. 18 (1987), 880883. MR 883574 (88f:05017)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199210735251
PII:
S 00029939(1992)10735251
Article copyright:
© Copyright 1992
American Mathematical Society
