θ-congruent numbers and elliptic curves

• Autorzy: Makiko Kan
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 94
• Numer: 2
• Strony: 153-160

Daty

wydano

2000

otrzymano

1998-11-24

poprawiono

1999-12-13

Twórcy

autor

Makiko Kan

• Department of Mathematics, Ochanomizu University, Otsuka, Tokyo 112-8610, Japan

Bibliografia

• [1] B. J. Birch, Elliptic curves and modular functions, in: Symposia Math. IV (Roma, 1968/69), Academic Press, 1970, 27-32.
• [2] B. J. Birch, Heegner points of elliptic curves, in: Symposia Math. XV (Roma, 1973), Academic Press, 1975, 441-445.
• [3] J. S. Chahal, On an identity of Desboves, Proc. Japan Acad. Ser. A 60 (1984), 105-108.
• [4] G. Frey, Some aspects of the theory of elliptic curves over number fields, Exposition. Math. 4 (1986), 35-66.
• [5] R. Fricke, Lehrbuch der Algebra III, Braunschweig, 1928.
• [6] M. Fujiwara, θ-congruent numbers, in: Number Theory, K. Győry, A. Pethő, and V. Sós (eds.), de Gruyter, 1997, 235-241.
• [7] B. Gross and D. Zagier, Heegner points and derivatives of L-series, Invent. Math. 84 (1986), 225-320.
• [8] P. Monsky, Mock Heegner points and congruent numbers, Math. Z. 204 (1990), 45-68.
• [9] P. Serf, Congruent numbers and elliptic curves, in: Computational Number Theory, A. Pethő et al. (eds.), de Gruyter, 1991, 227-238.
• [10] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986.
• [11] A. Wiman, Über den Rang von Kurven $y^2=x(x+a)(x+b)$, Acta Math. 76 (1944), 225-251.