Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture

Keqin Feng

Acta Arithmetica (1996)

  • Volume: 75, Issue: 1, page 71-83
  • ISSN: 0065-1036

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Keqin Feng. "Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture." Acta Arithmetica 75.1 (1996): 71-83. <http://eudml.org/doc/206863>.

@article{KeqinFeng1996,
author = {Keqin Feng},
journal = {Acta Arithmetica},
keywords = {non-congruent numbers; rational point; elliptic curve; Birch-Swinnerton-Dyer conjecture},
language = {eng},
number = {1},
pages = {71-83},
title = {Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture},
url = {http://eudml.org/doc/206863},
volume = {75},
year = {1996},
}

TY - JOUR
AU - Keqin Feng
TI - Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture
JO - Acta Arithmetica
PY - 1996
VL - 75
IS - 1
SP - 71
EP - 83
LA - eng
KW - non-congruent numbers; rational point; elliptic curve; Birch-Swinnerton-Dyer conjecture
UR - http://eudml.org/doc/206863
ER -

References

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  1. [1] R. Alter, T. B. Curtz and K. K. Kubota, Remarks and results on congruent numbers, in: Proc. 3rd South Eastern Conf. Combin., Graph Theory and Comput., 1972, Florida Atlantic Univ., Boca Raton, Fla., 1972, 27-35. Zbl0259.10010
  2. [2] J. E. Cremona and R. W. Odoni, Some density results for negative Pell equations; an application of graph theory, J. London Math. Soc. 39 (1989), 16-28. Zbl0678.10015
  3. [3] G. P. Gogišvili, The number of representations of numbers by positive quaternary diagonal quadratic forms, Sakharth SSR Mecn. Math. Inst. Šrom. 40 (1971), 59-105 (MR 49#2536 (=E28-203)) (in Russian). 
  4. [4] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer, 1984. Zbl0553.10019
  5. [5] J. Lagrange, Nombres congruents et courbes elliptiques, Sém. Delange-Pisot-Poitou, 16e année, 1974/75, no. 16. 
  6. [6] L. Rédei, Arithmetischer Beweis des Satzes über die Anzahl der durch vier teilbaren Invarianten der absoluten Klassengruppe im quadratischen Zahlkörper, J. Reine Angew. Math. 171 (1934), 55-60. Zbl60.0125.02
  7. [7] L. Rédei und H. Reichardt, Die Anzahl der durch 4 teilbaren Invarianten der Klassengruppe eines beliebigen quadratischen Zahlkörpers, J. Reine Angew. Math. 170 (1933), 69-74. Zbl59.0192.01
  8. [8] K. Rubin, Tate-Shafarevich group and L-functions of elliptic curves with complex multiplication, Invent. Math. 89 (1987), 527-560. Zbl0628.14018
  9. [9] K. Rubin, The main conjecture for imaginary quadratic fields, Invent. Math. 103 (1991), 25-68. Zbl0737.11030
  10. [10] P. Serf, Congruent numbers and elliptic curves, in: Computational Number Theory, A. Pethő, M. Pohst, H. C. Williams and H. G. Zimmer (eds.), de Gruyter, 1991, 227-238. Zbl0736.11017
  11. [11] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986. Zbl0585.14026
  12. [12] J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math. 72 (1983), 323-334. Zbl0515.10013

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