Integer points on curves of genus 1

Wolfgang M. Schmidt

Compositio Mathematica (1992)

  • Volume: 81, Issue: 1, page 33-59
  • ISSN: 0010-437X

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Schmidt, Wolfgang M.. "Integer points on curves of genus 1." Compositio Mathematica 81.1 (1992): 33-59. <http://eudml.org/doc/90132>.

@article{Schmidt1992,
author = {Schmidt, Wolfgang M.},
journal = {Compositio Mathematica},
keywords = {curves of genus 1; elliptic curves; integer points; height; Weierstrass curves},
language = {eng},
number = {1},
pages = {33-59},
publisher = {Kluwer Academic Publishers},
title = {Integer points on curves of genus 1},
url = {http://eudml.org/doc/90132},
volume = {81},
year = {1992},
}

TY - JOUR
AU - Schmidt, Wolfgang M.
TI - Integer points on curves of genus 1
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 81
IS - 1
SP - 33
EP - 59
LA - eng
KW - curves of genus 1; elliptic curves; integer points; height; Weierstrass curves
UR - http://eudml.org/doc/90132
ER -

References

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  1. [1] A. Baker: The diophantine equation y2=ax3+bx2+cx+d, J. London Math. Soc.43 (1968), 1-9. Zbl0155.08701MR231783
  2. [2] A. Baker: Bounds for the solutions of the hyperelliptic equation, Proc. Camb. Phil. Soc.65 (1969), 439-444. Zbl0174.33803MR234912
  3. [3] A. Baker: The theory of linear forms in logarithms. Transcendence theory: Advances and applications, Proceedings of 1976 Cambridge Conference, Academic Press (1977), pp. 1-27. Zbl0361.10028MR498417
  4. [4] A. Baker and J. Coates: Integer points on curves of genus 1, Proc. Camb. Phil. Soc.67 (1970), 595-602. Zbl0194.07601MR256983
  5. [5] E. Bombieri and J. Vaaler: On Siegel's lemma, Invent. Math.73 (1983), 11-32. Zbl0533.10030MR707346
  6. [6] J. Coates: Construction of rational functions on a curve, Proc. Camb. Phil. Soc.68 (1970), 105-123. Zbl0215.37302MR258831
  7. [7] M. Deuring: Lectures on the theory of algebraic functions of one variable, Springer Lecture Notes314 (1973). Zbl0249.14008MR344231
  8. [8] E. Dobrowolski: On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith.34 (1979), 391-401. Zbl0416.12001MR543210
  9. [9] J.H. Evertse and J.H. Silverman: Uniform bounds for the number of solutions to Yn=f(X), Math. Proc. Camb. Phil. Soc.100 (1986), 237-248. Zbl0611.10009MR848850
  10. [10] K. Györy: On the solutions of linear diophantine equations in algebraic integers of bounded norm. Ann. Univ. Budapest, Eötvös, Sect. Math.22-23 (1979/80), 225-233. Zbl0442.10010MR588441
  11. [11] E. Hecke: Vorlesungen über die Theorie der Algebraischen Zahlen, Akademische Verlagsges, Leipzig (1923). JFM49.0106.10
  12. [12] S. Lang: Algebraic Numbers, Addison-Wesley Publ. Co. (1964). Zbl0211.38501MR160763
  13. [13] S. Lang: Fundamentals of Diophantine Geometry, Springer-Verlag (1983). Zbl0528.14013MR715605
  14. [14] P. Philippon and M. Waldschmidt: Lower Bounds for Linear Forms in Logarithms, (New advances in transcendence theory, 1986 symposium, Durham), Cambridge University Press (1988). Zbl0659.10037MR972007
  15. [15] W.M. Schmidt: Eisenstein's theorem on power series expansions of algebraic functions, Acta Arith.56 (1990), 161-179. Zbl0659.12003MR1075642
  16. [16] W.M. Schmidt: Construction and estimation of bases in function fields, J. Number Theory (to appear). Zbl0764.11046MR1129568
  17. [17] C.L. Siegel (under the pseudoname X): The integer solutions of the equation y2=axn+bxn-1+...+k, J. London Math. Soc.1 (1926), 66-68. JFM52.0149.02
  18. [18] C.L. Siegel: Abschätzung von Einheiten, Nachr. Akad. d. Wiss.Göttingen, Math.-Phys. Kl. (1969), 71-86 (Collected Works, No. 88). Zbl0186.36703MR249395
  19. [19] J.H. Silverman: The arithmetic of elliptic curves, Springer Graduate Texts106 (1986). Zbl0585.14026MR817210
  20. [20] J.H. Silverman: Lower bounds for height functions, Duke Math. J.51 (1984), 395-403. Zbl0579.14035MR747871
  21. [21] V.G. Sprinžuk:Hyperelliptic diophantine equations and the number of ideal classes, Acta. Arith.30 (1976), 95-108 (in Russian). Zbl0335.10021MR417050
  22. [22] G. Wüstholz: A New Approach to Baker's Theorem on Linear Forms in Logarithms III, (New advances in transcendence theory, 1986 symposium, Durham), Cambridge University Press. Zbl0659.10036

Citations in EuDML Documents

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  1. Dimitrios Poulakis, Points entiers sur les courbes hyperelliptiques
  2. Dimitrios Poulakis, Points entiers sur les courbes de genre 0
  3. Dimitrios Poulakis, The number of solutions of the Mordell equation
  4. Yann Bugeaud, Kálmán Győry, Bounds for the solutions of Thue-Mahler equations and norm form equations
  5. J. Gebel, A. Pethő, H. G. Zimmer, Computing integral points on elliptic curves
  6. Roelof J. Stroeker, Benjamin M. M. de Weger, Solving elliptic diophantine equations: the general cubic case
  7. Dimitrios Poulakis, Estimation effective des points entiers d'une famille de courbes algébriques
  8. Yann Bugeaud, Kálmán Győry, Bounds for the solutions of unit equations

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