# Kloosterman sums and primitive elements in Galois fields

Acta Arithmetica (2000)

- Volume: 94, Issue: 2, page 173-201
- ISSN: 0065-1036

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top## How to cite

topCohen, Stephen. "Kloosterman sums and primitive elements in Galois fields." Acta Arithmetica 94.2 (2000): 173-201. <http://eudml.org/doc/207430>.

@article{Cohen2000,

author = {Cohen, Stephen},

journal = {Acta Arithmetica},

keywords = {Galois fields; trace function; primitive element; character sums; Gauss sums; generalized Kloosterman sums},

language = {eng},

number = {2},

pages = {173-201},

title = {Kloosterman sums and primitive elements in Galois fields},

url = {http://eudml.org/doc/207430},

volume = {94},

year = {2000},

}

TY - JOUR

AU - Cohen, Stephen

TI - Kloosterman sums and primitive elements in Galois fields

JO - Acta Arithmetica

PY - 2000

VL - 94

IS - 2

SP - 173

EP - 201

LA - eng

KW - Galois fields; trace function; primitive element; character sums; Gauss sums; generalized Kloosterman sums

UR - http://eudml.org/doc/207430

ER -

## References

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- [Co2] S. D. Cohen, Gauss sums and a sieve for generators of Galois fields, Publ. Math. Debrecen 56 (2000) (Kálmán Győry 60th birthday issue), to appear.
- [CoHa1] S. D. Cohen and D. Hachenberger, Primitive normal bases with prescribed trace, Appl. Algebra Engrg. Comm. Comput. 9 (1999), 383-403. Zbl0931.12002
- [CoHa2] S. D. Cohen and D. Hachenberger, Primitivity, freeness, norm and trace, Discrete Math. 214 (2000), 135-144.
- [Ha] W. B. Han, The coefficients of primitive polynomials over finite fields, Math. Comp. 65 (1996), 331-340. Zbl0865.11081
- [HaMu] T. Hansen and G. L. Mullen, Primitive polynomials over finite fields, ibid. 59 (1992), 639-643. Zbl0770.11053
- [Ju] D. Jungnickel, Finite Fields. Structures and Arithmetics, Bibliographisches Institut, Mannheim, 1993.
- [JuVu] D. Jungnickel and S. A. Vanstone, On primitive polynomials over finite fields, J. Algebra 124 (1989), 337-353. Zbl0694.12013
- [LiNi] R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Reading, MA, 1983; 2nd ed., Cambridge Univ. Press, Cambridge, 1997. Zbl0554.12010
- [MoMu] I. H. Morgan and G. L. Mullen, Primitive normal polynomials over finite fields, Math. Comp. 63 (1994), 759-765. Zbl0805.11083
- [Mu] G. L. Mullen, Bases and the distribution of irreducible and primitive polynomials over finite fields, in: Applications of Finite Fields, Inst. Math. Appl. Conf. Ser. New Ser. 59, 1996, 1-18. Zbl0877.11068
- [Ni] H. Niederreiter, An enumeration formula for certain irreducible polynomials with an application to the construction of irreducible polynomials over the binary fields, Appl. Algebra Engrg. Comm. Comput. 1 (1990), 119-124. Zbl0726.11077

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