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

Acta Arithmetica (1997)

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

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topDae 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

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

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