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On the average rank of LYM-sets

✍ Scribed by Péter L. Erdős; Ulrich Faigle; Walter Kern

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 431 KB
Volume: 144
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00282-n

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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