Predictive criteria for the representation of primes by binary quadratic forms

• Autorzy: Joseph B. Muskat , Blair K. Spearman , Kenneth S. Williams
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 70
• Numer: 3
• Strony: 215-278

Daty

wydano

1995

otrzymano

1994-05-18

Twórcy

autor

Joseph B. Muskat

• Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel

autor

Blair K. Spearman

• Department of Mathematics, Okanagan University College, Kelowna, British Columbia, Canada V1Y 4X8

autor

Kenneth S. Williams

• Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6

Bibliografia

• [1] S. Arno, The imaginary quadratic fields of class number 4, Acta Arith. 60 (1992), 321-334.
• [2] P. Barrucand and H. Cohn, Note on primes of type x² + 32y², class number, and residuacity, J. Reine Angew. Math. 238 (1969), 67-70.
• [3] J. A. Brandler, Residuacity properties of real quadratic units, J. Number Theory 5 (1973), 271-286.
• [4] E. Brown, The power of 2 dividing the class-number of a binary quadratic discriminant, J. Number Theory 5 (1973), 413-419.
• [5] E. Brown, Class numbers of quadratic fields, Istituto Nazionale di alta Matematica, Symposia Mathematica (Bologna) 15 (1975), 403-411.
• [6] H. Cohn, A Second Course in Number Theory, Wiley, New York, 1962.
• [7] P. E. Conner and J. Hurrelbrink, Class Number Parity, World Sci., Singapore, 1988.
• [8] D. A. Cox, Primes of the Form x² + ny²; Fermat, Class Field Theory and Complex Multiplication, Wiley, New York, 1989.
• [9] P. G. L. Dirichlet, Recherches sur les diviseurs premiers d'une classe de formules du quatrième degré, J. Reine Angew. Math. 3 (1828), 35-69.
• [10] D. R. Estes and G. Pall, A reconsideration of Legendre-Jacobi symbols, J. Number Theory 5 (1973), 433-434.
• [11] C. F. Gauss, Disquisitiones Arithmeticae, English translation by Arthur A. Clarke, Yale University Press, 1966.
• [12] R. H. Hudson and K. S. Williams, Congruences for representations of primes by binary quadratic forms, Acta Arith. 41 (1982), 311-322.
• [13] P. Kaplan, K. S. Williams, and Y. Yamamoto, An application of dihedral fields to representations of primes by binary quadratic forms, Acta Arith. 44 (1984), 407-413.
• [14] P. A. Leonard and K. S. Williams, A representation problem involving binary quadratic forms, Arch. Math. (Basel) 36 (1981), 53-56.
• [15] J. B. Muskat, On simultaneous representations of primes by binary quadratic forms, J. Number Theory 19 (1984), 263-282.
• [16] J. B. Muskat and A. L. Whiteman, The cyclotomic numbers of order twenty, Acta Arith. 17 (1970), 185-216.
• [17] L. Rédei and H. Reichardt, Die Anzahl der durch 4 teilbaren Invarianten der Klassengruppe eines beliebigen quadratischen Zahlkörpers, J. Reine Angew. Math. 170 (1933), 69-74