Cyclotomic numbers of order 2l, l an odd prime

Vinaykumar Acharya; S. Katre

ArticleOriginal scientific text

Title

Cyclotomic numbers of order 2l, l an odd prime

Authors ¹, ²

Affiliations

Department of Mathematics, Fergusson College, Pune-411004, India
Department of Mathematics, University of Poona, Pune-411007, India

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

Title

Cyclotomic numbers of order 2l, l an odd prime

Affiliations

Bibliography