Imaginary quadratic fields with small odd class number

• Autorzy: Steven Arno , M. L. Robinson , Ferrell S. Wheeler
• Języki publikacji: EN

Słowa kluczowe

EN

binary quadratic forms   imaginary quadratic fields   class numbers   discriminants  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 83
• Numer: 4
• Strony: 295-330

Daty

wydano

1998

otrzymano

1995-03-13

poprawiono

1996-12-15

Twórcy

autor

Steven Arno

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

autor

M. L. Robinson

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

autor

Ferrell S. Wheeler

• 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.