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Average Root Numbers for a Nonconstant Family of Elliptic Curves

โœ Scribed by Ottavio G. Rizzo

Book ID
110423846
Publisher
Cambridge University Press
Year
2003
Tongue
English
Weight
316 KB
Volume
136
Category
Article
ISSN
0010-437X

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๐Ÿ“œ SIMILAR VOLUMES

The Average Analytic Rank of a Family of
The Average Analytic Rank of a Family of Elliptic Curves
โœ L. Mai ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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