The Analytic Rank of a Family of Jacobians of Fermat Curves

• Autorzy: Tomasz Jędrzejak
• Języki publikacji: EN

Abstrakty

EN

We study the family of curves $F_{m}(p): x^{p} + y^{p} = m$, 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 $F_{m}(p)$. 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.

Kategorie tematyczne

• 11G35: Varieties over global fields
• 11G10: Abelian varieties of dimension > 1
• 11G40: L -functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: 56
• Numer: 3
• Strony: 199-206

Daty

wydano

2008

Twórcy

autor

Tomasz Jędrzejak

• Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

Identyfikatory

DOI

10.4064/ba56-3-2