# The number of solutions of the Mordell equation

Acta Arithmetica (1999)

- Volume: 88, Issue: 2, page 173-179
- ISSN: 0065-1036

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top## How to cite

topDimitrios Poulakis. "The number of solutions of the Mordell equation." Acta Arithmetica 88.2 (1999): 173-179. <http://eudml.org/doc/207237>.

@article{DimitriosPoulakis1999,

author = {Dimitrios Poulakis},

journal = {Acta Arithmetica},

keywords = {Mordell equation; number of solutions; cubic diophantine equation; elliptic curves},

language = {eng},

number = {2},

pages = {173-179},

title = {The number of solutions of the Mordell equation},

url = {http://eudml.org/doc/207237},

volume = {88},

year = {1999},

}

TY - JOUR

AU - Dimitrios Poulakis

TI - The number of solutions of the Mordell equation

JO - Acta Arithmetica

PY - 1999

VL - 88

IS - 2

SP - 173

EP - 179

LA - eng

KW - Mordell equation; number of solutions; cubic diophantine equation; elliptic curves

UR - http://eudml.org/doc/207237

ER -

## References

top- [1] A. Brumer and J. Silverman, The number of elliptic curves over ℚ with conductor N, Manuscripta Math. 91 (1996), 95-102. Zbl0868.11029
- [2] J. H. Evertse, On equations in S-units and the Thue-Mahler equation, Invent. Math. 75 (1984), 561-584. Zbl0521.10015
- [3] J. H. Evertse and J. H. Silverman, Uniform bounds for the number of solutions to ${Y}^{m}=f\left(X\right)$, Math. Proc. Cambridge Philos. Soc. 100 (1986), 237-248. Zbl0611.10009
- [4] H. Hasse, Number Theory, Springer, Berlin, 1980.
- [5] S. Lang, Elliptic Functions, Addison-Wesley, 1973.
- [6] P. Llorente and E. Nart, Effective determination of the decomposition of the rational primes in a cubic field, Proc. Amer. Math. Soc. 87 (1983), 579-585. Zbl0514.12003
- [7] W. M. Schmidt, Integer points on curves of genus 1, Compositio Math. 81 (1992), 33-59. Zbl0747.11026
- [8] J. H. Silverman, The Arithmetic of Elliptic Curves, Grad. Texts in Math. 106, Springer, New York, 1986.

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