Cyclotomic numbers of order 2l, l an odd prime

• Autorzy: Vinaykumar V. Acharya , S. A. Katre
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 69
• Numer: 1
• Strony: 51-74

Daty

wydano

1995

otrzymano

1993-07-02

poprawiono

1994-05-05

Twórcy

autor

Vinaykumar V. Acharya

• Department of Mathematics, Fergusson College, Pune-411004, India

autor

S. A. Katre

• Department of Mathematics, University of Poona, Pune-411007, India

Bibliografia

• [1] B. C. Berndt and R. J. Evans, Sums of Gauss, Eisenstein, Jacobi, Jacobsthal and Brewer, Illinois J. Math. 23 (1979), 374-437.
• [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] L. E. Dickson, Cyclotomy, higher congruences, and Waring's problem, Amer. J. Math. 57 (1935), 391-424.
• [4] L. E. Dickson, Cyclotomy and trinomial congruences, Trans. Amer. Math. Soc. 37 (1935), 363-380.
• [5] M. Hall, Cyclotomy and characters, in: Proc. Sympos. Pure Math. 8, Amer. Math. Soc., 1965, 31-43.
• [6] S. A. Katre and A. R. Rajwade, Complete solution of the cyclotomic problem in $𝔽*_q$ for any prime modulus l, $q = p^α$, p≡ 1 (mod l), Acta Arith. 45 (1985), 183-199.
• [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.
• [8] J. B. Muskat, The cyclotomic numbers of order fourteen, Acta Arith. 11 (1966), 263-279.
• [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.
• [10] T. Storer, On the unique determination of the cyclotomic numbers for Galois fields and Galois domains, J. Combin. Theory 2 (1967), 296-300.
• [11] A. L. Whiteman, Cyclotomic numbers of order 10, in: Proc. Sympos. Appl. Math. 10, Amer. Math. Soc., 1960, 95-111.
• [12] Y. C. Zee, Jacobi sums of order 22, Proc. Amer. Math. Soc. 28 (1971), 25-31