Cyclotomic numbers of order 2l, l an odd prime

Vinaykumar V. Acharya; S. A. Katre

Acta Arithmetica (1995)

  • Volume: 69, Issue: 1, page 51-74
  • ISSN: 0065-1036

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Vinaykumar V. Acharya, and S. A. Katre. "Cyclotomic numbers of order 2l, l an odd prime." Acta Arithmetica 69.1 (1995): 51-74. <http://eudml.org/doc/206672>.

@article{VinaykumarV1995,
author = {Vinaykumar V. Acharya, S. A. Katre},
journal = {Acta Arithmetica},
keywords = {finite fields; cyclotomic numbers; Jacobi sums; diophantine system},
language = {eng},
number = {1},
pages = {51-74},
title = {Cyclotomic numbers of order 2l, l an odd prime},
url = {http://eudml.org/doc/206672},
volume = {69},
year = {1995},
}

TY - JOUR
AU - Vinaykumar V. Acharya
AU - S. A. Katre
TI - Cyclotomic numbers of order 2l, l an odd prime
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 1
SP - 51
EP - 74
LA - eng
KW - finite fields; cyclotomic numbers; Jacobi sums; diophantine system
UR - http://eudml.org/doc/206672
ER -

References

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  2. [2] N. Buck and K. S. Williams, Sequel to Muskat's evaluation of the cyclotomic numbers of order fourteen, Carleton Mathematical Series 216, November 1985, Carleton University, Ottawa, 22 pp. 
  3. [3] L. E. Dickson, Cyclotomy, higher congruences, and Waring's problem, Amer. J. Math. 57 (1935), 391-424. Zbl0012.01203
  4. [4] L. E. Dickson, Cyclotomy and trinomial congruences, Trans. Amer. Math. Soc. 37 (1935), 363-380. Zbl0011.29301
  5. [5] M. Hall, Cyclotomy and characters, in: Proc. Sympos. Pure Math. 8, Amer. Math. Soc., 1965, 31-43. 
  6. [6] S. A. Katre and A. R. Rajwade, Complete solution of the cyclotomic problem in for any prime modulus l, , p≡ 1 (mod l), Acta Arith. 45 (1985), 183-199. Zbl0525.12015
  7. [7] S. A. Katre and A. R. Rajwade, Resolution of the sign ambiguity in the determination of the cyclotomic numbers of order 4 and the corresponding Jacobsthal sum, Math. Scand. 60 (1987), 52-62. Zbl0602.12005
  8. [8] J. B. Muskat, The cyclotomic numbers of order fourteen, Acta Arith. 11 (1966), 263-279. Zbl0139.28101
  9. [9] J. C. Parnami, M. K. Agrawal and A. R. Rajwade, Jacobi sums and cyclotomic numbers for a finite field, Acta Arith. 41 (1982), 1-13. Zbl0491.12019
  10. [10] T. Storer, On the unique determination of the cyclotomic numbers for Galois fields and Galois domains, J. Combin. Theory 2 (1967), 296-300. Zbl0154.04903
  11. [11] A. L. Whiteman, Cyclotomic numbers of order 10, in: Proc. Sympos. Appl. Math. 10, Amer. Math. Soc., 1960, 95-111. 
  12. [12] Y. C. Zee, Jacobi sums of order 22, Proc. Amer. Math. Soc. 28 (1971), 25-31 Zbl0213.32901

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