An "Anti-Hasse Principle" for Prime Twists
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
Given an algebraic curve C/Q having points everywhere locally and endowed with a suitable involution, we show that there exists a positive density family of prime quadratic twists of C violating the Hasse principle. The result applies in particular to w_N-Atkin-Lehner twists of most modular curves X_0(N) and to w_p-Atkin-Lehner twists of certain Shimura curves X^{D+}.
Cite
@article{arxiv.math/0609465,
title = {An "Anti-Hasse Principle" for Prime Twists},
author = {Pete L. Clark},
journal= {arXiv preprint arXiv:math/0609465},
year = {2007}
}
Comments
9 pages