The Analytic Rank of a Family of Jacobians of Fermat Curves

Tomasz Jędrzejak. "The Analytic Rank of a Family of Jacobians of Fermat Curves." Bulletin of the Polish Academy of Sciences. Mathematics 56.3 (2008): 199-206. <http://eudml.org/doc/281282>.

@article{TomaszJędrzejak2008,
abstract = {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.},
author = {Tomasz Jędrzejak},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {twisted Fermat curves; hyperelliptic curves; Jacobian variety; -function; root number; analytic rank},
language = {eng},
number = {3},
pages = {199-206},
title = {The Analytic Rank of a Family of Jacobians of Fermat Curves},
url = {http://eudml.org/doc/281282},
volume = {56},
year = {2008},
}

TY - JOUR
AU - Tomasz Jędrzejak
TI - The Analytic Rank of a Family of Jacobians of Fermat Curves
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2008
VL - 56
IS - 3
SP - 199
EP - 206
AB - 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.
LA - eng
KW - twisted Fermat curves; hyperelliptic curves; Jacobian variety; -function; root number; analytic rank
UR - http://eudml.org/doc/281282
ER -