Gauss sums for orthogonal groups over a finite field of characteristic two

Dae San Kim; Young Ho Park

Acta Arithmetica (1997)

  • Volume: 82, Issue: 4, page 331-357
  • ISSN: 0065-1036

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Dae San Kim, and Young Ho Park. "Gauss sums for orthogonal groups over a finite field of characteristic two." Acta Arithmetica 82.4 (1997): 331-357. <http://eudml.org/doc/207096>.

@article{DaeSanKim1997,
author = {Dae San Kim, Young Ho Park},
journal = {Acta Arithmetica},
keywords = {Gauss sum; multiplicative character; additive character; orthogonal group; Kloosterman sum; Bruhat decomposition; maximal parabolic subgroup; Clifford algebra; finite field; Gauss sums; special orthogonal groups; Kloosterman sums},
language = {eng},
number = {4},
pages = {331-357},
title = {Gauss sums for orthogonal groups over a finite field of characteristic two},
url = {http://eudml.org/doc/207096},
volume = {82},
year = {1997},
}

TY - JOUR
AU - Dae San Kim
AU - Young Ho Park
TI - Gauss sums for orthogonal groups over a finite field of characteristic two
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 4
SP - 331
EP - 357
LA - eng
KW - Gauss sum; multiplicative character; additive character; orthogonal group; Kloosterman sum; Bruhat decomposition; maximal parabolic subgroup; Clifford algebra; finite field; Gauss sums; special orthogonal groups; Kloosterman sums
UR - http://eudml.org/doc/207096
ER -

References

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  1. [1] A. A. Albert, Symmetric and alternate matrices in an arbitrary field I, Trans. Amer. Math. Soc. 43 (1938), 386-436. Zbl0018.34202
  2. [2] P. G. Buckhiester, Gauss sums and the number of solutions to the matrix equation X A X T = 0 over G F ( 2 y ) , Acta Arith. 23 (1973), 271-278. Zbl0233.15014
  3. [3] D. S. Kim, Gauss sums for general and special linear groups over a finite field, Arch. Math. (Basel), to appear. Zbl1036.11528
  4. [4] D. S. Kim, Gauss sums for O(2n+1,q), submitted. Zbl0937.11058
  5. [5] D. S. Kim, Gauss sums for O¯(2n,q), Acta Arith. 80 (1997), 343-365. 
  6. [6] D. S. Kim, Gauss sums for U(2n,q²), Glasgow Math. J., to appear. 
  7. [7] D. S. Kim, Gauss sums for U(2n+1,q²), submitted. Zbl1036.11527
  8. [8] D. S. Kim, Gauss sums for symplectic groups over a finite field, Monatsh. Math., to appear. Zbl1036.11529
  9. [9] D. S. Kim and I.-S. Lee, Gauss sums for O⁺(2n,q), Acta Arith. 78 (1996), 75-89. 
  10. [10] F. J. MacWilliams, Orthogonal matrices over finite fields, Amer. Math. Monthly 76 (1969), 152-164. Zbl0186.33702
  11. [11] Z.-X. Wan, Geometry of Classical Groups over Finite Fields, Studentlitteratur, Lund, 1993. Zbl0817.51001

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