Predictive criteria for the representation of primes by binary quadratic forms

Joseph B. Muskat; Blair K. Spearman; Kenneth S. Williams

Acta Arithmetica (1995)

  • Volume: 70, Issue: 3, page 215-278
  • ISSN: 0065-1036

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Joseph B. Muskat, Blair K. Spearman, and Kenneth S. Williams. "Predictive criteria for the representation of primes by binary quadratic forms." Acta Arithmetica 70.3 (1995): 215-278. <http://eudml.org/doc/206750>.

@article{JosephB1995,
author = {Joseph B. Muskat, Blair K. Spearman, Kenneth S. Williams},
journal = {Acta Arithmetica},
keywords = {predictive criteria; binary quadratic forms},
language = {eng},
number = {3},
pages = {215-278},
title = {Predictive criteria for the representation of primes by binary quadratic forms},
url = {http://eudml.org/doc/206750},
volume = {70},
year = {1995},
}

TY - JOUR
AU - Joseph B. Muskat
AU - Blair K. Spearman
AU - Kenneth S. Williams
TI - Predictive criteria for the representation of primes by binary quadratic forms
JO - Acta Arithmetica
PY - 1995
VL - 70
IS - 3
SP - 215
EP - 278
LA - eng
KW - predictive criteria; binary quadratic forms
UR - http://eudml.org/doc/206750
ER -

References

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  1. [1] S. Arno, The imaginary quadratic fields of class number 4, Acta Arith. 60 (1992), 321-334. Zbl0760.11033
  2. [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. Zbl0207.36202
  3. [3] J. A. Brandler, Residuacity properties of real quadratic units, J. Number Theory 5 (1973), 271-286. Zbl0272.12002
  4. [4] E. Brown, The power of 2 dividing the class-number of a binary quadratic discriminant, J. Number Theory 5 (1973), 413-419. Zbl0273.12005
  5. [5] E. Brown, Class numbers of quadratic fields, Istituto Nazionale di alta Matematica, Symposia Mathematica (Bologna) 15 (1975), 403-411. 
  6. [6] H. Cohn, A Second Course in Number Theory, Wiley, New York, 1962. 
  7. [7] P. E. Conner and J. Hurrelbrink, Class Number Parity, World Sci., Singapore, 1988. 
  8. [8] D. A. Cox, Primes of the Form x² + ny²; Fermat, Class Field Theory and Complex Multiplication, Wiley, New York, 1989. 
  9. [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. [10] D. R. Estes and G. Pall, A reconsideration of Legendre-Jacobi symbols, J. Number Theory 5 (1973), 433-434. Zbl0268.10004
  11. [11] C. F. Gauss, Disquisitiones Arithmeticae, English translation by Arthur A. Clarke, Yale University Press, 1966. 
  12. [12] R. H. Hudson and K. S. Williams, Congruences for representations of primes by binary quadratic forms, Acta Arith. 41 (1982), 311-322. Zbl0493.10007
  13. [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. Zbl0553.10018
  14. [14] P. A. Leonard and K. S. Williams, A representation problem involving binary quadratic forms, Arch. Math. (Basel) 36 (1981), 53-56. Zbl0437.10009
  15. [15] J. B. Muskat, On simultaneous representations of primes by binary quadratic forms, J. Number Theory 19 (1984), 263-282. Zbl0547.10003
  16. [16] J. B. Muskat and A. L. Whiteman, The cyclotomic numbers of order twenty, Acta Arith. 17 (1970), 185-216. Zbl0216.30801
  17. [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 Zbl59.0192.01

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