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December 2018 On the Integral Representation of Binary Quadratic Forms and the Artin Condition
Yingpu DENG, Chang LV, Junchao SHENTU
Tokyo J. Math. 41(2): 371-384 (December 2018). DOI: 10.3836/tjm/1502179249

Abstract

For diophantine equations of the form $ax^2+bxy+cy^2+g=0$ over $\mathbb{Z}$ whose coefficients satisfy some assumptions, we show that a condition with respect to the 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.

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Yingpu DENG. Chang LV. Junchao SHENTU. "On the Integral Representation of Binary Quadratic Forms and the Artin Condition." Tokyo J. Math. 41 (2) 371 - 384, December 2018. https://doi.org/10.3836/tjm/1502179249

Information

Published: December 2018
First available in Project Euclid: 20 November 2017

zbMATH: 07053482
MathSciNet: MR3908800
Digital Object Identifier: 10.3836/tjm/1502179249

Subjects:
Primary: 11D09, 11D57, 11E12
Secondary: 11R37, 14L30

Rights: Copyright © 2018 Publication Committee for the Tokyo Journal of Mathematics

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Vol.41 • No. 2 • December 2018
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