Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

On the class number of imaginary quadratic fields


Author: A. Baker
Journal: Bull. Amer. Math. Soc. 77 (1971), 678-684
MSC (1970): Primary 12A25, 12A50; Secondary 10F35
DOI: https://doi.org/10.1090/S0002-9904-1971-12768-4
MathSciNet review: 0286775
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. E. A. Anfert'eva and N. G.Čudakov, Minima of the norm function in imaginary quadratic fields, Dokl. Akad. Nauk SSSR 183 (1968), 255-256= Soviet Math. Dokl. 9 (1968), 1342-1344. MR 39 #5472.
  • 2. E. A. Anfert'eva and N. G.Čudakov, Effective lower bounds for the minimum of the norm of ideals in quadratic fields, Mat. Sb. 82 (1970), 55-66 =Math. USSR Sb. 11 (1970), 47-58. MR 271063
  • 3. A. Baker, Linear forms in the logarithms of algebraic numbers. I, II, III, IV, Mathematika 13 (1966), 204-216; ibid. 14 (1967), 102-107, 220-228; ibid. 15 (1968), 204-216. MR 36 #3732. MR 258756
  • 4. A. Baker, Contributions to the theory of Diophantine equations. I. On the representation of integers by binary forms; II. The Diophantine equation y2=x3+k, Philos. Trans. Roy. Soc. London Ser. A 263 (1967/68), 173-208. MR 37 #4005; 4006. MR 228424
  • 5. A. Baker, A remark on the class number of quadratic fields, Bull. London Math. Soc. 1 (1969), 98-102. MR 39 #2723. MR 241383
  • 6. A. Baker, Imaginary quadratic fields with class number 2, Ann. of Math, (to appear). MR 299583
  • 7. A. Baker, A sharpening of thè bounds for linear forms in logarithms, Acta Arith. (to appear).
  • 8. A. Baker and A. Schinzel, On the least integers represented by the genera of binary quadratic forms, Acta Arith. (to appear). MR 319896
  • 9. A. Baker and H. Stark, On a fundamental inequality in number theory, Ann. of Math, (to appear).
  • 10. R. Brauer, On the zeta-functions of algebraic number fields, Amer. J. Math. 69 (1947), 243-250. MR 8, 567. MR 20597
  • 11. A. O. Gel'fond, Transcendental and algebraic numbers, GITTL, Moscow, 1952; English transl., Dover, New York, 1960. MR 15, 292; MR 22 #2598. MR 111736
  • 12. A. O. Gel'fond and Yu. V. Linnik, On Thue's method in the problem of effectiveness in quadratic fields, Dokl. Akad. Nauk SSSR 61 (1948), 773-776. (Russian) MR 10, 354. MR 27783
  • 13. K. Heegner, Diophantische Analysis und Modulfunktionen, Math. Z. 56 (1952), 227-253. MR 14, 725. MR 53135
  • 14. H. Heilbronn, On the class number in imaginary quadratic fields, Quart. J. Math. Oxford Ser. 5 (1934), 150-160.
  • 15. H. Heilbronn and E. H. Linfoot, On the imaginary quadratic corpora of class number one, Quart. J. Math. Oxford Ser. 5 (1934), 293-301.
  • 16. C. L. Siegel, Über die Classenzahl quadratischer Zahlkorper, Acta Arith. 1 (1935), 83-86; Ges. Abhandlungen I, 406-409.
  • 17. H. M. Stark, On complex quadratic fields with class-number equal to one, Trans. Amer. Math. Soc. 122 (1966), 112-119. MR 195845
  • 18. H. M. Stark, A complete determination of the complex quadratic fields of class-number one, Michigan Math. J. 14 (1967), 1-27. MR 36 #5102. MR 222050
  • 19. H. M. Stark, A transcendence theorem for class-number problems, Ann. of Math, (to appear). MR 297715

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 12A25, 12A50, 10F35

Retrieve articles in all journals with MSC (1970): 12A25, 12A50, 10F35


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1971-12768-4

American Mathematical Society