Exponential sums for symplectic groups and their applications

Dae San Kim

Acta Arithmetica (1999)

  • Volume: 88, Issue: 2, page 155-171
  • ISSN: 0065-1036

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Dae San Kim. "Exponential sums for symplectic groups and their applications." Acta Arithmetica 88.2 (1999): 155-171. <http://eudml.org/doc/207236>.

@article{DaeSanKim1999,
author = {Dae San Kim},
journal = {Acta Arithmetica},
keywords = {exponential sum; additive character; symplectic group; Bruhat decomposition; maximal parabolic subgroup; exponential sums; symplectic groups; multiple Kloosterman sums; Gauss sums; trace},
language = {eng},
number = {2},
pages = {155-171},
title = {Exponential sums for symplectic groups and their applications},
url = {http://eudml.org/doc/207236},
volume = {88},
year = {1999},
}

TY - JOUR
AU - Dae San Kim
TI - Exponential sums for symplectic groups and their applications
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 2
SP - 155
EP - 171
LA - eng
KW - exponential sum; additive character; symplectic group; Bruhat decomposition; maximal parabolic subgroup; exponential sums; symplectic groups; multiple Kloosterman sums; Gauss sums; trace
UR - http://eudml.org/doc/207236
ER -

References

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  1. [1] B. C. Berndt and R. J. Evans, Sums of Gauss, Jacobi, and Jacobsthal, J. Number Theory 11 (1979), 349-398. 
  2. [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. [3] B. C. Berndt and R. J. Evans, The determination of Gauss sums, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 107-129. Zbl0471.10028
  4. [4] L. Carlitz, Representation by skew forms in a finite field, Arch. Math. (Basel) 5 (1954), 19-31. Zbl0056.01702
  5. [5] J. H. Hodges, Exponential sums for skew matrices in a finite field, Arch. Math. 7 (1956), 116-121. Zbl0071.01702
  6. [6] J. H. Hodges, Weighted partitions for skew matrices over a finite field, Arch. Math. 8 (1957), 16-22. Zbl0080.01202
  7. [7] D. S. Kim, Gauss sums for general and special linear groups over a finite field, Arch. Math. 69 (1997), 297-304. Zbl1036.11528
  8. [8] D. S. Kim, Gauss sums for symplectic groups over a finite field, Monatsh. Math. 126 (1998), 55-71. Zbl1036.11529
  9. [9] D. S. Kim, Gauss sums for O¯(2n,q), Acta Arith. 80 (1997), 343-365. 
  10. [10] D. S. Kim, Gauss sums for O(2n+1,q), Finite Fields Appl. 4 (1998), 62-86. Zbl0937.11058
  11. [11] D. S. Kim, Gauss sums for U(2n,q²), Glasgow Math. J. 40 (1998), 79-95. Zbl0915.11061
  12. [12] D. S. Kim, Gauss sums for U(2n+1,q²), J. Korean Math. Soc. 34 (1997), 871-894 . Zbl1036.11527
  13. [13] D. S. Kim and I.-S. Lee, Gauss sums for O⁺(2n,q), Acta Arith. 78 (1996), 75-89. 
  14. [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. [15] D. H. and E. Lehmer, On the cubes of Kloosterman sums, Acta Arith. 6 (1960), 15-22. Zbl0092.04701
  16. [16] D. H. and E. Lehmer, The cyclotomy of Kloosterman sums, Acta Arith. 12 (1967), 385-407. Zbl0149.28603
  17. [17] R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl. 20, Cambridge Univ. Press, Cambridge, 1987. 
  18. [18] H. Salié, Über die Kloostermanschen Summen S(u,v;q), Math. Z. 34 (1932), 91-109. 

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