A class of diophantine equations connected with certain elliptic curves over Q ( - 13 )

R. J. Stroeker

Compositio Mathematica (1979)

  • Volume: 38, Issue: 3, page 329-346
  • ISSN: 0010-437X

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Stroeker, R. J.. "A class of diophantine equations connected with certain elliptic curves over $Q(\sqrt{-13})$." Compositio Mathematica 38.3 (1979): 329-346. <http://eudml.org/doc/89408>.

@article{Stroeker1979,
author = {Stroeker, R. J.},
journal = {Compositio Mathematica},
keywords = {Elliptic Curves with Good Reduction; Imaginary Quadratic Number Fields; Diophantine Equations; Bad Reduction},
language = {eng},
number = {3},
pages = {329-346},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {A class of diophantine equations connected with certain elliptic curves over $Q(\sqrt\{-13\})$},
url = {http://eudml.org/doc/89408},
volume = {38},
year = {1979},
}

TY - JOUR
AU - Stroeker, R. J.
TI - A class of diophantine equations connected with certain elliptic curves over $Q(\sqrt{-13})$
JO - Compositio Mathematica
PY - 1979
PB - Sijthoff et Noordhoff International Publishers
VL - 38
IS - 3
SP - 329
EP - 346
LA - eng
KW - Elliptic Curves with Good Reduction; Imaginary Quadratic Number Fields; Diophantine Equations; Bad Reduction
UR - http://eudml.org/doc/89408
ER -

References

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  1. [1] Z.I. Borevich and I.R. Shafarevich: Number Theory. Pure and Appl. Maths. Ser.20. Acad. Press, New York and London, 1966. Zbl0145.04902MR195803
  2. [2] B. Delaunay: Ueber die Darstellung der Zahlen durch die binäre kubische Formen mit negativer Diskriminante. Math. Zeitschr.31 (1930) 1-26. MR1545095JFM55.0722.02
  3. [3] P. Déligne: Courbes elliptiques: Formulaire (d'après J. Tate). In: Modular functions of one variable IV. Lecture Notes in Maths.476. Springer, Berlin-Heidelberg -New York, 1975, 53-73. MR387292
  4. [4] L.J. Mordell: Diophantine Equations. Pure and Appl. Maths. Ser.30. Acad. Press, New York and London, 1969. Zbl0188.34503MR249355
  5. [5] T. Nagell: Darstellungen ganzer Zahlen durch binäre kubische Formen mit negativer Diskriminante. Math. Zeitschr.28 (1928) 10-29. Zbl54.0174.02MR1544935JFM54.0174.02
  6. [6] C.L. Siegel: Ueber einige Anwendungen Diophantischer Approximationen. Abh. Preuss. Akad. Wiss. Phys.-Math. Kl.1929 nr. 1. JFM56.0180.05
  7. [7] R.J. Stroeker: Elliptic curves defined over imaginary quadratic number fields. Doct. thesis, Univ. Amsterdam, 1975. Zbl0342.14014MR450290
  8. [8] J.T. Tate: Letter to J.-P. Serre, dated July 24th 1971. 

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