Exponential sums for symplectic groups and their applications

• Autorzy: Dae San Kim
• Języki publikacji: EN

Słowa kluczowe

EN

exponential sum; additive character; symplectic group; Bruhat decomposition; maximal parabolic subgroup

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: 1999
• Tom: 88
• Numer: 2
• Strony: 155-171

Daty

wydano

1999

otrzymano

1998-02-20

poprawiono

1998-10-23

Twórcy

autor

Dae San Kim

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

Bibliografia

• [1] B. C. Berndt and R. J. Evans, Sums of Gauss, Jacobi, and Jacobsthal, J. Number Theory 11 (1979), 349-398.
• [2] B. C. Berndt and R. J. Evans, Sums of Gauss, Eisenstein, Jacobi, and Jacobsthal, and Brewer, Illinois J. Math. 23 (1979), 374-437.
• [3] B. C. Berndt and R. J. Evans, The determination of Gauss sums, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 107-129.
• [4] L. Carlitz, Representation by skew forms in a finite field, Arch. Math. (Basel) 5 (1954), 19-31.
• [5] J. H. Hodges, Exponential sums for skew matrices in a finite field, Arch. Math. 7 (1956), 116-121.
• [6] J. H. Hodges, Weighted partitions for skew matrices over a finite field, Arch. Math. 8 (1957), 16-22.
• [7] D. S. Kim, Gauss sums for general and special linear groups over a finite field, Arch. Math. 69 (1997), 297-304.
• [8] D. S. Kim, Gauss sums for symplectic groups over a finite field, Monatsh. Math. 126 (1998), 55-71.
• [9] D. S. Kim, Gauss sums for O¯(2n,q), Acta Arith. 80 (1997), 343-365.
• [10] D. S. Kim, Gauss sums for O(2n+1,q), Finite Fields Appl. 4 (1998), 62-86.
• [11] D. S. Kim, Gauss sums for U(2n,q²), Glasgow Math. J. 40 (1998), 79-95.
• [12] D. S. Kim, Gauss sums for U(2n+1,q²), J. Korean Math. Soc. 34 (1997), 871-894 .
• [13] D. S. Kim and I.-S. Lee, Gauss sums for O⁺(2n,q), Acta Arith. 78 (1996), 75-89.
• [14] D. S. Kim and Y. H. Park, Gauss sums for orthogonal groups over a finite field of characteristic two, Acta Arith. 82 (1997), 331-357.
• [15] D. H. and E. Lehmer, On the cubes of Kloosterman sums, Acta Arith. 6 (1960), 15-22.
• [16] D. H. and E. Lehmer, The cyclotomy of Kloosterman sums, Acta Arith. 12 (1967), 385-407.
• [17] R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl. 20, Cambridge Univ. Press, Cambridge, 1987.
• [18] H. Salié, Über die Kloostermanschen Summen S(u,v;q), Math. Z. 34 (1932), 91-109.