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1998 | 84 | 4 | 291-335
Tytuł artykułu

On the theory of cubic residues and nonresidues

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
84
Numer
4
Strony
291-335
Opis fizyczny
Daty
wydano
1998
otrzymano
1994-11-21
poprawiono
1997-09-08
Twórcy
autor
  • Department of Mathematics, Huaiyin Teachers College, Huaiyin 223001, Jiangsu, People's Republic of China
Bibliografia
  • [Ba] Ph. Barkan, Partitions quadratiques et cyclotomie, Sém. Delange-Pisot-Poitou (1975), Zbl324:10037.
  • [Bu] K. Burde, Zur Herleitung von Reziprozitätsgesetzen unter Benutzung von endlichen Körpern, J. Reine Angew. Math. 293/294 (1977), 418-427, MR57:16178.
  • [Ca] C. Cailler, Sur les congruences du troisième degré, Enseign. Math. 10 (1908), 474-487.
  • [C] A. Cauchy, Sur la résolution des équivalences dont les modules se réduisent à des nombres premiers, Exercises de Mathématiques 4 (1829), 253-292.
  • [CG] A. Cunningham and T. Gosset, 4-tic and 3-bic residuacity-tables, Messenger Math. 50 (1920), 1-30.
  • [D] L. E. Dickson, History of the Theory of Numbers, Vol. I, Chelsea, New York, 1952, 393-407.
  • [FR] E. T. Federighi and R. G. Roll, Fibonacci Quart. (1966), 85-88.
  • [HW] R. H. Hudson and K. S. Williams, Resolution of ambiguities in the evaluation of cubic and quartic Jacobsthal sums, Pacific J. Math. 99 (1982), 379-386.
  • [IR] K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, New York, 1982.
  • [J] J. G. D. Jacobi, De residuis cubicis commentatio numerosa, J. Reine Angew. Math. 2 (1827), 66-69.
  • [K] L. Kronecker, Werke, Vol. II, 93 and 97-101; Vol. IV, 123-129, Chelsea, New York, 1968.
  • [L1] E. Lehmer, Criteria for cubic and quartic residuacity, Mathematika 5 (1958), 20-29.
  • [L2] E. Lehmer, On Euler's criterion, J. Austral. Math. Soc. 1 (1959/1961, part 1), 64-70, MR21:7191.
  • [L3] E. Lehmer, On the cubic character of quadratic units, J. Number Theory 5 (1973), 385-389, MR48:271.
  • [L4] E. Lehmer, On the quartic character of quadratic units, J. Reine Angew. Math. 268/269 (1974), 294-301.
  • [L5] E. Lehmer, On the number of solutions of $u^k + D ≡ w (mod p)$, Pacific J. Math. 5 (1955), 103-118.
  • [L6] E. Lehmer, On the quadratic character of the Fibonacci root, Fibonacci Quart. 4 (1966), 135-138, MR39:160.
  • [Li] H. von Lienen, Reelle kubische und biquadratische Legendre-Symbole, J. Reine Angew. Math. 305 (1979), 140-154.
  • [R] P. Ribenboim, The Book of Prime Number Records, 2nd ed., Springer, Berlin, 1989, 44-50.
  • [Sh] D. Shanks, On Gauss and composition I, in: Number Theory and Applications (edited by R. A. Mollin), Dordrecht, Boston, 1989, 163-178, MR92e:11150.
  • [SW] B. K. Spearman and K. S. Williams, The cubic congruence x³ + Ax² + Bx + C ≡ 0 (mod p) and binary quadratic forms, J. London Math. Soc. (2) 46 (1992), 397-410, MR93j:11004.
  • [St] L. Stickelberger, Über eine neue Eigenschaft der Diskriminanten algebraischer Zahlkörper, Verhand. I. Internat. Math. Kongress (1897), Zürich, 182-193.
  • [S1] Z. H. Sun, Combinatorial sum $∑^{n}_{k=}_{k≡ r(mod m)} {n \choose k}$ and its applications in number theory II, J. Nanjing Univ. Biquarterly 10 (1993), 105-118, MR94j:11021.
  • [S2] Z. H. Sun, Supplements to the theory of biquadratic residues, submitted.
  • [SS] Z. H. Sun and Z. W. Sun, Fibonacci numbers and Fermat's last theorem, Acta Arith. 60 (1992), 371-388.
  • [We] P. J. Weinberger, The cubic character of quadratic units, Proc. 1972 Number Theory Conference, Univ. of Colorado, 1972, 241-242, MR52:10673.
  • [W1] K. S. Williams, On Euler's criterion for cubic non-residues, Proc. Amer. Math. Soc. 49 (1975), 277-283.
  • [W2] K. S. Williams, Cubic nonresidues (mod p), Delta 6 (1976), 23-28, MR54:5095.
  • [WH] K. S. Williams and R. H. Hudson, Representation of primes by the principal form of discriminant -D when the class number h(-D) is 3, Acta Arith. 57 (1991), 131-153.
Typ dokumentu
Bibliografia
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