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International Algorithmic Number Theory Symposium

ANTS 2002: Algorithmic Number Theory pp 198–204Cite as

Integral Points on Punctured Abelian Surfaces

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2369))

Abstract

We study the density of integral points on punctured abelian surfaces. Linear growth rates are observed experimentally.

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References

  1. Bogomolov, F.A., Tschinkel, Yu.: Density of rational points on elliptic K3 surfaces. Asian J. Math. 4 (2000) 351–368

    MATH  MathSciNet  Google Scholar 

  2. Cantor, D.G.: On the analogue of the division polynomials for hyperelliptic curves. J. Reine Angew. Math. 447 (1994) 91–145

    MATH  MathSciNet  Google Scholar 

  3. Flynn, E.V.: Descent via isogeny in dimension 2. Acta Arith. 66 (1994) 23–43

    MATH  MathSciNet  Google Scholar 

  4. Gordon, D.M., Grant, D.: Computing the Mordell-Weil rank of Jacobians of curves of genus two. Trans. Amer. Math. Soc. 337 (1993) 807–824

    Article  MATH  MathSciNet  Google Scholar 

  5. Gupta, R., Murty, M.R.: Cyclicity and generation of points mod p on elliptic curves. Invent. Math. 101 (1990) 225–235

    Article  MATH  MathSciNet  Google Scholar 

  6. Harris, J., Tschinkel, Yu.: Rational points on quartics. Duke Math. J. 104 (2000) 477–500

    Article  MATH  MathSciNet  Google Scholar 

  7. Hassett, B., Tschinkel, Yu.: Density of integral points on algebraic varieties. In: Peyre, E., Tschinkel, Yu. (eds.): Rational Points on Algebraic Varieties. Progr. Math., Vol. 199. Birkhäuser, Basel (2001) 169–197

    Google Scholar 

  8. Lang, S., Trotter, H.: Primitive points on elliptic curves. Bull. Amer. Math. Soc. 83 (1977) 289–292

    Article  MATH  MathSciNet  Google Scholar 

  9. Serre, J.-P.: Propriétés galoisiennes des points d’ordre fini des courbes elliptiques. Invent. Math. 15 (1972) 259–331

    Article  MATH  MathSciNet  Google Scholar 

  10. Vojta, P.: Diophantine approximation and value distribution theory. Lecture Notes in Math., Vol. 1239. Springer-Verlag, Berlin (1987)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104

    Andrew Kresch & Yuri Tschinkel

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544

    Andrew Kresch & Yuri Tschinkel

Authors
  1. Andrew Kresch
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  2. Yuri Tschinkel
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Editor information

Editors and Affiliations

  1. School of Mathematics and Statistics, F07, University of Sydney, Sydney, NSW, 2006, Australia

    Claus Fieker  & David R. Kohel  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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Kresch, A., Tschinkel, Y. (2002). Integral Points on Punctured Abelian Surfaces. In: Fieker, C., Kohel, D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45455-1_16

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  • DOI: https://doi.org/10.1007/3-540-45455-1_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43863-2

  • Online ISBN: 978-3-540-45455-7

  • eBook Packages: Springer Book Archive

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