On the Integral Representation of Binary Quadratic Forms and the Artin Condition
Number Theory
2019-12-18 v2
Abstract
For diophantine equations of the form ax^2+bxy+cy^2+g=0 over Z whose coefficients satisfy some assumptions, we show that a condition with respect to Artin reciprocity map, which we call the Artin condition, is the only obstruction to the local-global principle for integral solutions of the equation. Some concrete examples are presented.
Keywords
Cite
@article{arxiv.1510.04800,
title = {On the Integral Representation of Binary Quadratic Forms and the Artin Condition},
author = {Chang Lv and Junchao Shentu and Yingpu Deng},
journal= {arXiv preprint arXiv:1510.04800},
year = {2019}
}
Comments
11 pages, git commit 20150803a/3b8df3d. arXiv admin note: substantial text overlap with arXiv:1502.07457