Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A character sum for root system $ G\sb 2$

Author: Ronald Evans
Journal: Proc. Amer. Math. Soc. 114 (1992), 627-635
MSC: Primary 11L05; Secondary 11T24, 17B20, 17B25, 33C80
MathSciNet review: 1073525
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A character sum analog of the Macdonald-Morris constant term identity for the root system $ {G_2}$ 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.

References [Enhancements On Off] (What's this?)

  • [1] G. W. Anderson, The evaluation of Selberg sums, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), 469-472. MR 1076474 (91m:11109)
  • [2] R. J. Evans, Identities for products of Gauss sums over finite fields, Enseign. Math. (2) 27 (1981), 197-209. MR 659148 (83i:10050)
  • [3] -, Character sum analogues of constant term identities for root systems, Israel J. Math. 46 (1983), 189-196. 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), 111-128. MR 975841 (90e:11120)
  • [6] F. G. Garvan, A beta integral associated with the root system $ {G_2}$, SIAM J. Math. Anal. 19 (1988), 1462-1474. 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, Springer-Verlag, New York, 1982. MR 661047 (83g:12001)
  • [9] I. G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal. 13 (1982), 988-1007. 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 $ {G_2}$ case of Macdonald's root system--Dyson conjecture, SIAM J. Math. Anal. 18 (1987), 880-883. MR 883574 (88f:05017)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11L05, 11T24, 17B20, 17B25, 33C80

Retrieve articles in all journals with MSC: 11L05, 11T24, 17B20, 17B25, 33C80

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society