Download PDF - Imaginary quadratic fields with small odd class numberAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Imaginary quadratic fields with small odd class number

Authors 1, 1, 1

Affiliations

  1. Center for Computing Sciences, 17100 Science Drive, Bowie, Maryland 20715, U.S.A.

Keywords

ENG
binary quadratic forms, imaginary quadratic fields, class numbers, discriminants

Bibliography

  1. S. Arno, The imaginary quadratic fields of class number 4, Acta Arith. 60 (1992), 321-334.
  2. A. Baker, Linear forms in the logarithms of algebraic numbers. I, Mathematika 13 (1966), 204-216.
  3. A. Baker, Imaginary quadratic fields with class number 2, Ann. of Math. 94 (1971), 139-152.
  4. A. Baker, Transcendental Number Theory, Cambridge Univ. Press, New York, 1975.
  5. B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves. II, J. Reine Angew. Math. 218 (1965), 79-108.
  6. D. A. Buell, Class groups of quadratic fields. II, Math. Comp. 48 (1987), 85-93.
  7. H. Davenport, Multiplicative Number Theory, 2nd ed., Grad. Texts in Math. 74, Springer, New York, 1980.
  8. M. Deuring, Imaginäre quadratische Zahlkörper mit der Klassenzahl Eins, Invent. Math. 5 (1968), 169-179.
  9. C. F. Gauss, Disquisitiones Arithmeticae, Yale Univ. Press, 1966.
  10. D. M. Goldfeld, The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer, Ann. Scuola Norm. Sup. Pisa 3 (1976), 623-663.
  11. B. Gross et D. Zagier, Points de Heegner et derivées de fonctions L, C. R. Acad. Sci. Paris 297 (1983), 85-87.
  12. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford Univ. Press, London, 1968.
  13. K. Heegner, Diophantische Analysis und Modulfunktionen, Math. Z. 56 (1952), 227-253.
  14. H. Heilbronn, On the class number in imaginary quadratic fields, Quart. J. Math. Oxford Ser. 25 (1934), 150-160.
  15. A. E. Ingham, The Distribution of Prime Numbers, Cambridge Tracts in Math. 30, Cambridge Univ. Press, Cambridge, 1990.
  16. H. Kestelman, Modern Theories of Integration, Dover, New York, 1960.
  17. N. Levinson and R. M. Redheffer, Complex Variables, Holden-Day, San Francisco, 1970.
  18. H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, Acta Arith. 24 (1974), 529-542.
  19. J. Oesterlé, Nombres de classes des corps quadratiques imaginaires, Sém. Bourbaki, 1983-1984, exp. 631.
  20. C. L. Siegel, Über die Classenzahl quadratischer Zahlkörper, Acta Arith. 1 (1936), 83-86.
  21. C. L. Siegel, Zum Beweise des Starkschen Satzes, Invent. Math. 5 (1968), 180-191.
  22. H. M. Stark, On complex quadratic number fields with class number equal to one, Trans. Amer. Math. Soc. 122 (1966), 112-119.
  23. H. M. Stark, A complete determination of the complex quadratic fields of class number one, Michigan Math. J. 14 (1967), 1-27.
  24. H. M. Stark, On the 'gap' in a theorem of Heegner, J. Number Theory 1 (1969), 16-27.
  25. H. M. Stark, L-functions and character sums for quadratic forms (II), Acta Arith. 15 (1969), 307-317.
  26. H. M. Stark, A transcendence theorem for class number problems, Ann. of Math. 94 (1971), 153-173.
  27. H. M. Stark, On a transcendence theorem for class number problems II, Ann. of Math. 96 (1972), 251-259.
  28. H. M. Stark, On complex quadratic fields with class number two, Math. Comp. 29 (1975), 289-302.
  29. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge Univ. Press, London, 1966.
  30. A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204-220.
  31. P. J. Weinberger, On small zeros of Dirichlet L-functions, Math. Comp. 29 (1975), 319-328.
Acta Arithmetica
1998/83/4
Export to PBN, Opens in new tab
Pages:
295-330
Main language of publication
English
Received
1995-03-13
Accepted
1996-12-15
Published
1998
Exact and natural sciences