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

• Autorzy: Dae San Kim , Young Ho Park
• Języki publikacji: EN

Słowa kluczowe

EN

Gauss sum; multiplicative character; additive character; orthogonal group; Kloosterman sum; Bruhat decomposition; maximal parabolic subgroup; Clifford algebra

Kategorie tematyczne

• 11T23: Exponential sums
• 11T24: Other character sums and Gauss sums
• 20G40: Linear algebraic groups over finite fields
• 20H30: Other matrix groups over finite fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 82
• Numer: 4
• Strony: 331-357

Daty

wydano

1997

otrzymano

1997-01-17

Twórcy

autor

Dae San Kim

• Department of Mathematics, Sogang University, Seoul 121-742, Korea

autor

Young Ho Park

• Department of Mathematics, Kangwon National University, Chuncheon 200-701, Korea

Bibliografia

• [1] A. A. Albert, Symmetric and alternate matrices in an arbitrary field I, Trans. Amer. Math. Soc. 43 (1938), 386-436.
• [2] P. G. Buckhiester, Gauss sums and the number of solutions to the matrix equation $XAX^T = 0$ over $GF(2^y)$, Acta Arith. 23 (1973), 271-278.
• [3] D. S. Kim, Gauss sums for general and special linear groups over a finite field, Arch. Math. (Basel), to appear.
• [4] D. S. Kim, Gauss sums for O(2n+1,q), submitted.
• [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.
• [8] D. S. Kim, Gauss sums for symplectic groups over a finite field, Monatsh. Math., to appear.
• [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.
• [11] Z.-X. Wan, Geometry of Classical Groups over Finite Fields, Studentlitteratur, Lund, 1993.