The Analytic Rank of a Family of Jacobians of Fermat Curves
Tomasz Jędrzejak
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008), p. 199-206 / Harvested from The Polish Digital Mathematics Library
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We study the family of curves Fm(p):xp+yp=m, where p is an odd prime and m is a pth 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 Fm(p). As a corollary we conclude that the jacobians of the curves Fm(5) with even analytic rank and those with odd analytic rank are equally distributed.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:281282 
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     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {56},
     year = {2008},
     pages = {199-206},
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     language = {en},
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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) pp. 199-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-3-2/