Gauss sums for O⁺(2n,q)

Dae San Kim; In-Sok Lee

Acta Arithmetica (1996)

  • Volume: 78, Issue: 1, page 75-89
  • ISSN: 0065-1036

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Dae San Kim, and In-Sok Lee. "Gauss sums for O⁺(2n,q)." Acta Arithmetica 78.1 (1996): 75-89. <http://eudml.org/doc/206933>.

@article{DaeSanKim1996,
author = {Dae San Kim, In-Sok Lee},
journal = {Acta Arithmetica},
keywords = {orthogonal group; Bruhat decomposition; maximal parabolic subgroup; multiplicative character; additive character; finite field; Gauss sums; Kloosterman sums},
language = {eng},
number = {1},
pages = {75-89},
title = {Gauss sums for O⁺(2n,q)},
url = {http://eudml.org/doc/206933},
volume = {78},
year = {1996},
}

TY - JOUR
AU - Dae San Kim
AU - In-Sok Lee
TI - Gauss sums for O⁺(2n,q)
JO - Acta Arithmetica
PY - 1996
VL - 78
IS - 1
SP - 75
EP - 89
LA - eng
KW - orthogonal group; Bruhat decomposition; maximal parabolic subgroup; multiplicative character; additive character; finite field; Gauss sums; Kloosterman sums
UR - http://eudml.org/doc/206933
ER -

References

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  1. [1] L. Carlitz, Weighted quadratic partitions over a finite field, Canad. J. Math. 5 (1953), 317-323. Zbl0052.03805
  2. [2] L. Carlitz, Representations by quadratic forms in a finite field, Duke Math. J. 21 (1954), 123-137. Zbl0055.01301
  3. [3] L. E. Dickson, Linear Groups with an Exposition of the Galois Field Theory, Teubner, Leipzig, 1901. Zbl32.0128.01
  4. [4] J. H. Hodges, Exponential sums for symmetric matrices in a finite field, Math. Nachr. 14 (1955), 331-339. Zbl0072.00903
  5. [5] J. H. Hodges, Weighted partitions for symmetric matrices in a finite field, Math. Z. 66 (1956), 13-24. Zbl0080.01201
  6. [6] J. H. Hodges, Weighted partitions for general matrices over a finite field, Duke Math. J. 23 (1956), 545-552. Zbl0072.26702
  7. [7] J. H. Hodges, Weighted partitions for skew matrices over a finite field, Arch. Math. (Basel) 8 (1957), 16-22. Zbl0080.01202
  8. [8] J. H. Hodges, Weighted partitions for Hermitian matrices over a finite field, Math. Nachr. 17 (1958), 93-100. Zbl0084.04501
  9. [9] D. S. Kim, Gauss sums for O¯(2n,q), submitted. Zbl0937.11058
  10. [10] D. S. Kim, Gauss sums for O(2n+1,q), submitted. Zbl0937.11058
  11. [11] D. S. Kim, Gauss sums for symplectic groups over a finite field, submitted. Zbl1036.11529
  12. [12] R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl. 20, Cambridge University Press, Cambridge, 1987. 
  13. [13] F. J. MacWilliams, Orthogonal matrices over finite fields, Amer. Math. Monthly 76 (1969), 152-164. Zbl0186.33702
  14. [14] Z.-X. Wan, Geometry of Classical Groups over Finite Fields, Studentlitteratur, Lund, 1993. Zbl0817.51001

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