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ArticleOriginal scientific text

Title

Predictive criteria for the representation of primes by binary quadratic forms

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel
  2. Department of Mathematics, Okanagan University College, Kelowna, British Columbia, Canada V1Y 4X8
  3. Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6

Bibliography

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  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.
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  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
Acta Arithmetica
1995/70/3
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Pages:
215-278
Main language of publication
English
Received
1994-05-18
Published
1995
Exact and natural sciences