Geodesic
The Analytic Rank of a Family of Jacobians of Fermat Curves
Tomasz Jędrzejak1
1 Institute of Mathematics University of Szczecin Wielkopolska 15 70-451 Szczecin, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 3, pp. 199-206.

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We study the family of curves $F_{m}( p) :x^{p}+y^{p}=m$, where $p$ is an odd prime and $m$ is a $p$th power free integer. We prove some results about the distribution of root numbers of the $L$-functions of the hyperelliptic curves associated to the curves $F_{m}(p) $. As a corollary we conclude that the jacobians of the curves $F_{m}( 5) $ with even analytic rank and those with odd analytic rank are equally distributed.
DOI : 10.4064/ba56-3-2
Keywords: study family curves where odd prime pth power integer prove results about distribution root numbers l functions hyperelliptic curves associated curves corollary conclude jacobians curves even analytic rank those odd analytic rank equally distributed

Tomasz Jędrzejak 1

1 Institute of Mathematics University of Szczecin Wielkopolska 15 70-451 Szczecin, Poland 
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Tomasz Jędrzejak. The Analytic Rank of a Family of Jacobians of Fermat Curves. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 3, pp. 199-206. doi : 10.4064/ba56-3-2. http://geodesic.mathdoc.fr/articles/10.4064/ba56-3-2/

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