AN "ANTI-HASSE PRINCIPLE" FOR PRIME TWISTS-Reference-Cited by-同舟云学术

AN "ANTI-HASSE PRINCIPLE" FOR PRIME TWISTS

Published:2008-08 Issue:04 Volume:04 Page:627-637
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

CLARK PETE L.¹

Affiliation:

1. Department of Mathematics, University of Georgia, Athens, GA 30602-7403, USA

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 wN-Atkin–Lehner twists of most modular curves X0(N) and to wp-Atkin–Lehner twists of certain Shimura curves XD+.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042108001572

Reference11 articles.

1. Bielliptic Modular Curves

2. On large Picard groups and the Hasse Principle for curves and K3 surfaces

3. ℚ-Curves and Galois Representations

4. Genus zero translates of three point ramified galois extensions

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