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Integer points and the rank of Thue elliptic curves

✍ Scribed by Joseph H. Silverman


Publisher
Springer-Verlag
Year
1982
Tongue
English
Weight
381 KB
Volume
66
Category
Article
ISSN
0020-9910

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The Average Analytic Rank of a Family of
✍ L. Mai πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 333 KB

This paper studies the family of elliptic curves \(E_{m}: X^{3}+Y^{3}=m\) where \(m\) is a cubefree integer. Assuming the Generalized Rieman Hypothesis, the average rank of \(E_{m}\) 's with even analytic rank is proved to be \(\leqslant 5 / 2\), asymptotically. We also obtain some results for the c