Quadratic integral solutions to double Pell equations

Francesco Veneziano

Rendiconti del Seminario Matematico della Università di Padova (2011)

  • Volume: 126, page 47-61
  • ISSN: 0041-8994

How to cite

top

Veneziano, Francesco. "Quadratic integral solutions to double Pell equations." Rendiconti del Seminario Matematico della Università di Padova 126 (2011): 47-61. <http://eudml.org/doc/242037>.

@article{Veneziano2011,
author = {Veneziano, Francesco},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Pell equations; S-unit equations},
language = {eng},
pages = {47-61},
publisher = {Seminario Matematico of the University of Padua},
title = {Quadratic integral solutions to double Pell equations},
url = {http://eudml.org/doc/242037},
volume = {126},
year = {2011},
}

TY - JOUR
AU - Veneziano, Francesco
TI - Quadratic integral solutions to double Pell equations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2011
PB - Seminario Matematico of the University of Padua
VL - 126
SP - 47
EP - 61
LA - eng
KW - Pell equations; S-unit equations
UR - http://eudml.org/doc/242037
ER -

References

top
  1. [AH91] D. Abramovich - J. Harris, Abelian varieties and curves in W d ( C ) , Compositio Math., 78, 2 (1991), pp. 227–238. Zbl0748.14010MR1104789
  2. [CZ03] P. Corvaja - U. Zannier, On the number of integral points on algebraic curves, J. Reine Angew. Math., 565 (2003), pp. 27–42. Zbl1153.11315MR2024644
  3. [CZ04] P. Corvaja - U. Zannier, On integral points on surfaces, Ann. of Math. (2), 160, 2 (2004), pp. 705–726. Zbl1146.11035MR2123936
  4. [DF93] O. Debarre - R. Fahlaoui, Abelian varieties in W d r ( C ) and points of bounded degree on algebraic curves, Compositio Math., 88, 3 (1993), pp. 235–249. Zbl0808.14025MR1241949
  5. [EE93] Edited by B. Edixhoven - J.-H. Evertse, Diophantine approximation and abelian varieties, Lecture Notes in Mathematics, vol. 1566, Springer-Verlag, Berlin (1993), Introductory lectures, Papers from the conference held in Soesterberg, April 12–16, 1992. Zbl0811.14019MR1288998
  6. [Eve95] J.-H. Evertse, The number of solutions of decomposable form equations, Invent. Math., 122, 3 (1995), pp. 559–601. Zbl0851.11019MR1359604
  7. [HS91] J. Harris - J. Silverman, Bielliptic curves and symmetric products, Proc. Amer. Math. Soc., 112, 2 (1991), pp. 347–356. Zbl0727.11023MR1055774
  8. [Mah35] K. Mahler, On the lattice points on curves of genus 1, Proc. London Math. Soc., 39 (1935), pp. 431–466. Zbl61.0146.02JFM61.0146.02
  9. [Mor69] L. J. Mordell, Diophantine equations, Pure and Applied Mathematics, Vol. 30, Academic Press, London (1969). Zbl0188.34503MR249355
  10. [NW02] J. Noguchi - J. Winkelmann, Holomorphic curves and integral points off divisors, Math. Z., 239, 3 (2002), pp. 593–610. Zbl1011.32012MR1893854
  11. [Ser88] J.-P. Serre, Algebraic groups and class fields, Graduate Texts in Mathematics, vol. 117, Springer-Verlag, New York (1988), Translated from the French. Zbl0703.14001MR918564
  12. [Sil83] J. H. Silverman, Integer points on curves of genus 1 , J. London Math. Soc. (2), 28, 1 (1983), pp. 1–7. Zbl0487.10015MR703458
  13. [Voj87] P. Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin (1987). Zbl0609.14011MR883451
  14. [Voj91] P. Vojta, Arithmetic discriminants and quadratic points on curves, Arithmetic algebraic geometry (Texel, 1989), Progr. Math., vol. 89, Birkhäuser Boston, Boston, MA (1991), pp. 359–376. Zbl0749.14018MR1085268
  15. [Voj92] P. Vojta, A generalization of theorems of Faltings and Thue-Siegel-Roth-Wirsing, J. Amer. Math. Soc., 5, 4 (1992), pp. 763–804. Zbl0778.11037MR1151542
  16. [Voj96] P. Vojta, Integral points on subvarieties of semiabelian varieties. I, Invent. Math., 126, 1 (1996), pp. 133–181. Zbl1011.11040MR1408559
  17. [Wei07] A. Weil, Number theory, Modern Birkhäuser Classics, Birkhäuser Boston Inc., Boston, MA (2007), An approach through history from Hammurapi to Legendre, Reprint of the 1984 edition. Zbl1149.01013MR734177

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.