θ-congruent numbers and elliptic curves

Makiko Kan

Acta Arithmetica (2000)

  • Volume: 94, Issue: 2, page 153-160
  • ISSN: 0065-1036

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Kan, Makiko. "θ-congruent numbers and elliptic curves." Acta Arithmetica 94.2 (2000): 153-160. <http://eudml.org/doc/207428>.

@article{Kan2000,
author = {Kan, Makiko},
journal = {Acta Arithmetica},
keywords = {-congruent number; elliptic curve; Selmer group},
language = {eng},
number = {2},
pages = {153-160},
title = {θ-congruent numbers and elliptic curves},
url = {http://eudml.org/doc/207428},
volume = {94},
year = {2000},
}

TY - JOUR
AU - Kan, Makiko
TI - θ-congruent numbers and elliptic curves
JO - Acta Arithmetica
PY - 2000
VL - 94
IS - 2
SP - 153
EP - 160
LA - eng
KW - -congruent number; elliptic curve; Selmer group
UR - http://eudml.org/doc/207428
ER -

References

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  1. [1] B. J. Birch, Elliptic curves and modular functions, in: Symposia Math. IV (Roma, 1968/69), Academic Press, 1970, 27-32. Zbl1214.11081
  2. [2] B. J. Birch, Heegner points of elliptic curves, in: Symposia Math. XV (Roma, 1973), Academic Press, 1975, 441-445. 
  3. [3] J. S. Chahal, On an identity of Desboves, Proc. Japan Acad. Ser. A 60 (1984), 105-108. Zbl0562.14010
  4. [4] G. Frey, Some aspects of the theory of elliptic curves over number fields, Exposition. Math. 4 (1986), 35-66. Zbl0596.14022
  5. [5] R. Fricke, Lehrbuch der Algebra III, Braunschweig, 1928. Zbl54.0187.20
  6. [6] M. Fujiwara, θ-congruent numbers, in: Number Theory, K. Győry, A. Pethő, and V. Sós (eds.), de Gruyter, 1997, 235-241. 
  7. [7] B. Gross and D. Zagier, Heegner points and derivatives of L-series, Invent. Math. 84 (1986), 225-320. Zbl0608.14019
  8. [8] P. Monsky, Mock Heegner points and congruent numbers, Math. Z. 204 (1990), 45-68. Zbl0705.14023
  9. [9] P. Serf, Congruent numbers and elliptic curves, in: Computational Number Theory, A. Pethő et al. (eds.), de Gruyter, 1991, 227-238. Zbl0736.11017
  10. [10] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986. Zbl0585.14026
  11. [11] A. Wiman, Über den Rang von Kurven y 2 = x ( x + a ) ( x + b ) , Acta Math. 76 (1944), 225-251. Zbl0061.07109

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