Twisted Fermat curves over totally real fields
Number Theory
2007-06-05 v1
Abstract
Let p be a prime number, F a totally real field such that [F(mu_p): F]=2 and [F:Q] is odd. For delta \in F^times, let [delta] denote its class in F^times/F^{times p}. In this paper, we show Main Theorem. There are infinitely many classes [delta]\in F^times/F^{times p} such that the twisted affine Fermat curves W_delta: X^p+Y^p=delta have no F-rational points.
Keywords
Cite
@article{arxiv.0706.0470,
title = {Twisted Fermat curves over totally real fields},
author = {Adrian Diaconu and Ye Tian},
journal= {arXiv preprint arXiv:0706.0470},
year = {2007}
}