Determination of the two-class imaginary quadratic fields with an even discriminant by Heegner's method
In this article all the imaginary quadratic fields of even discriminant with class number 2 are determined by Heegner's method. These fields are obtained from the integral points of certain elliptic curves.
Unable to display preview. Download preview PDF.
- 1.A. Baker, “Linear forms in the logarithms of algebraic numbers,” Mathematika,13, 204–216 (1966).Google Scholar
- 2.H. M. Stark, “A complete determination of the complex quadratic fields of class-number one,” Michigan J. Math.,14, 1–27 (1967).Google Scholar
- 3.K. Heegner, “Diophantische Analysis und Modul-Funktionen,” Math. Zeit.,56, 227–253 (1952).Google Scholar
- 4.B. Birch, “Diophantine analysis and modular functions,” Collection of Translations, Matematika,15, No. 3, 173–178 (1971).Google Scholar
- 5.A. Baker, “Imaginary quadratic fields with class number 2,” Collection of Translations, Matematika,16, No. 5, 3–14 (1972).Google Scholar
- 6.M. A. Kenku, “Determination of the even discriminants of complex quadratic fields of class-number 2,” Proc. London Math. Soc.,22, 734–746 (1971).Google Scholar
- 7.B. Birch, “Invariants of Weber classes,” Collection of Translations, Matematika,15, No. 3, 179–192 (1971).Google Scholar
- 8.Z. I. Borevich and I. R. Shafarevich, Number Theory [in Russian], Moscow (1964).Google Scholar
- 9.L. J. Mordell, “On Lerch's class-number for binary quadratic forms,” Ark. Math.,5, 97–100 (1963–1965).Google Scholar
- 10.W. Ljunggren, “New solution of a problem proposed by Lucas,” Saetrtyke av Norsk, Math. Tidsskrift, 65–72 (1952).Google Scholar