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1998 | 83 | 4 | 295-330
Tytuł artykułu

Imaginary quadratic fields with small odd class number

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Czasopismo
Rocznik
Tom
83
Numer
4
Strony
295-330
Opis fizyczny
Daty
wydano
1998
otrzymano
1995-03-13
poprawiono
1996-12-15
Twórcy
autor
  • Center for Computing Sciences, 17100 Science Drive, Bowie, Maryland 20715, U.S.A.
  • Center for Computing Sciences, 17100 Science Drive, Bowie, Maryland 20715, U.S.A.
  • Center for Computing Sciences, 17100 Science Drive, Bowie, Maryland 20715, U.S.A.
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav83i4p295bwm
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