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The Average Analytic Rank of a Family of Elliptic Curves

✍ Scribed by L. Mai

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
333 KB
Volume
45
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 case of (E_{m}) 's with odd analytic rank and mean value theorems for higher moments of the analytic ranks. C 1993 Academic Press, Inc.

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