Download PDF - A complete generalization of Yokoi's p-invariantsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

A complete generalization of Yokoi's p-invariants

Authors 1, 2

Affiliations

  1. Department of Mathematics and Statistics , University of Calgary , Calgary, Alberta , Canada T2N 1N4
  2. Computer Science Department, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

Bibliography

  1. H. Cohn, A Second Course in Number Theory, Wiley, New York 1962.
  2. G. Degert, Über die Bestimmung der Grundeinheit gewisser reel-quadratischer Zahlkörper, Abh. Math. Sem. Univ. Hamburg 22 (1958), 92-97.
  3. H. Hasse, Über mehrklassige aber eingeschlechtige reel-quadratische Zahlkörper, Elemente Math. 20 (1965), 49-59.
  4. R. A. Mollin, On the insolubility of a class of Diophantine equations and the nontriviality of the class numbers of related real quadratic fields of Richaud-Degert type, Nagoya Math. J. 105 (1987), 39-47.
  5. R. A. Mollin, Class number one criteria for real quadratic fields I, Proc. Japan Acad. Ser. A 63 (1987), 121-125.
  6. R. A. Mollin and P. G. Walsh, A note on powerful numbers, quadratic fields and the pellian, C. R. Math. Rep. Acad. Sci. Canada 8 (1986), 109-114.
  7. R. A. Mollin and H. C. Williams, Prime producing quadratic polynomials and real quadratic fields of class number one, in: Number Theory, J. M. De Koninck and C. Levesque (eds.), Walter de Gruyter, Berlin 1989, 654-663.
  8. R. A. Mollin and H. C. Williams, Solution of the class number one problem for real quadratic fields of extended Richaud-Degert type (with one possible exception), in: Number Theory, R. A. Mollin (ed.), Walter de Gruyter, Berlin 1990, 417-425.
  9. R. A. Mollin and H. C. Williams, Class number one for real quadratic fields, continued fractions and reduced ideals, in: Number Theory and Applications, R. A. Mollin (ed.), NATO ASI Ser. C265, Kluwer, Dordrecht 1989, 481-496.
  10. R. A. Mollin and H. C. Williams, On prime valued polynomials and class numbers of real quadratic fields, Nagoya Math. J. 112 (1988), 143-151.
  11. T. Nagell, Number Theory, Chelsea, New York 1981.
  12. C. Richaud, Sur la résolution des équations x2-Ay2=±1, Atti Acad. Pontif. Nouvi Lincei (1866), 177-182.
  13. T. Tatuzawa, On a theorem of Siegel, Japan J. Math. 21 (1951), 163-178.
  14. H. Yokoi, New invariants of real quadratic fields, in: Number Theory, R. A. Mollin (ed.), Walter de Gruyter, Berlin 1990, 635-639.
  15. H. Yokoi, Class number one problem for real quadratic fields (The conjecture of Gauss), Proc. Japan Acad. Ser. A 64 (1988), 53-55.
  16. H. Yokoi, Some relations among new invariants of prime number p congruent to 1 (mod 4), in: Investigations in Number Theory, Adv. Stud. in Pure Math. 13, 1988, 493-501.
  17. H. Yokoi, The fundamental unit and class number one problem of real quadratic fields with prime discriminant, preprint.
  18. H. Yokoi, Bounds for fundamental units and class numbers of real quadratic fields with prime discriminant, preprint.
  19. H. Yokoi, On the fundamental unit of real quadratic fields with norm 1, J. Number Theory 2 (1970), 106-115.
  20. H. Yokoi, On real quadratic fields containing units with norm -1, Nagoya Math. J. 33 (1968), 139-152.
Colloquium Mathematicum
1992/63/2
Export to PBN, Opens in new tab
Pages:
285-294
Main language of publication
English
Received
1990-05-25
Accepted
1991-05-02
Published
1992
Exact and natural sciences