Geodesic
A bound for the average rank of a family of abelian varieties
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 241-252

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this note, we consider a one-parameter family of Abelian varieties $A/ \mathbb{Q}(T)$, 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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     author = {Wazir, Rania},
     title = {A bound for the average rank of a family of abelian varieties},
     journal = {Bollettino della Unione matematica italiana},
     pages = {241--252},
     publisher = {mathdoc},
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     year = {2004},
     zbl = {1118.11030},
     mrnumber = {MR2044269},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a10/}
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Wazir, Rania. A bound for the average rank of a family of abelian varieties. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 241-252. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a10/