A complete generalization of Yokoi's p-invariants

R. Mollin; H. Williams

Colloquium Mathematicae (1992)

  • Volume: 63, Issue: 2, page 285-294
  • ISSN: 0010-1354

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Mollin, R., and Williams, H.. "A complete generalization of Yokoi's p-invariants." Colloquium Mathematicae 63.2 (1992): 285-294. <http://eudml.org/doc/210153>.

@article{Mollin1992,
author = {Mollin, R., Williams, H.},
journal = {Colloquium Mathematicae},
keywords = {-invariants; -invariants; Gauss conjecture; Artin-Ankeny-Chowla conjecture; Mollin-Walsh conjecture; norm norm equations; quadratic fields; fundamental unit; class number one; Artin's conjecture},
language = {eng},
number = {2},
pages = {285-294},
title = {A complete generalization of Yokoi's p-invariants},
url = {http://eudml.org/doc/210153},
volume = {63},
year = {1992},
}

TY - JOUR
AU - Mollin, R.
AU - Williams, H.
TI - A complete generalization of Yokoi's p-invariants
JO - Colloquium Mathematicae
PY - 1992
VL - 63
IS - 2
SP - 285
EP - 294
LA - eng
KW - -invariants; -invariants; Gauss conjecture; Artin-Ankeny-Chowla conjecture; Mollin-Walsh conjecture; norm norm equations; quadratic fields; fundamental unit; class number one; Artin's conjecture
UR - http://eudml.org/doc/210153
ER -

References

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  1. [1] H. Cohn, A Second Course in Number Theory, Wiley, New York 1962. 
  2. [2] G. Degert, Über die Bestimmung der Grundeinheit gewisser reel-quadratischer Zahlkörper, Abh. Math. Sem. Univ. Hamburg 22 (1958), 92-97. Zbl0079.05803
  3. [3] H. Hasse, Über mehrklassige aber eingeschlechtige reel-quadratische Zahlkörper, Elemente Math. 20 (1965), 49-59. Zbl0128.03502
  4. [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. Zbl0591.12005
  5. [5] R. A. Mollin, Class number one criteria for real quadratic fields I, Proc. Japan Acad. Ser. A 63 (1987), 121-125. Zbl0625.12002
  6. [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. Zbl0595.10002
  7. [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. Zbl0695.12002
  8. [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. Zbl0696.12004
  9. [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. Zbl0714.11067
  10. [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. Zbl0629.12004
  11. [11] T. Nagell, Number Theory, Chelsea, New York 1981. 
  12. [12] C. Richaud, Sur la résolution des équations x 2 - A y 2 = ± 1 , Atti Acad. Pontif. Nouvi Lincei (1866), 177-182. 
  13. [13] T. Tatuzawa, On a theorem of Siegel, Japan J. Math. 21 (1951), 163-178. Zbl0054.02302
  14. [14] H. Yokoi, New invariants of real quadratic fields, in: Number Theory, R. A. Mollin (ed.), Walter de Gruyter, Berlin 1990, 635-639. Zbl0693.12004
  15. [15] H. Yokoi, Class number one problem for real quadratic fields (The conjecture of Gauss), Proc. Japan Acad. Ser. A 64 (1988), 53-55. Zbl0662.12006
  16. [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. [17] H. Yokoi, The fundamental unit and class number one problem of real quadratic fields with prime discriminant, preprint. Zbl0715.11057
  18. [18] H. Yokoi, Bounds for fundamental units and class numbers of real quadratic fields with prime discriminant, preprint. Zbl0715.11057
  19. [19] H. Yokoi, On the fundamental unit of real quadratic fields with norm 1, J. Number Theory 2 (1970), 106-115. Zbl0201.05703
  20. [20] H. Yokoi, On real quadratic fields containing units with norm -1, Nagoya Math. J. 33 (1968), 139-152. Zbl0167.04401

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