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A bound for the average rank of a family of abelian varieties

Rania Wazir — 2004

Bollettino dell'Unione Matematica Italiana

In this note, we consider a one-parameter family of Abelian varieties $A / Q (T)$ , and find an upper bound for the average rank in terms of the generic rank. This bound is based on Michel's estimates for the average rank in a one-parameter family of Abelian varieties, and extends previous work of Silverman for elliptic surfaces.

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