Integers of the Form $ax^2+bxy+cy^2$
Number Theory
2020-02-20 v3
Abstract
We provide a characterization of integers represented by the positive definite binary quadratic form . In order to prove the main theorem, we define the "relative conductor" of two orders in an imaginary quadratic field. Then we provide a characterization of decomposition of proper ideals of orders in imaginary quadratic fields. Moreover we present some interesting examples of the main theorem.
Keywords
Cite
@article{arxiv.2001.11632,
title = {Integers of the Form $ax^2+bxy+cy^2$},
author = {Naoki Uchida},
journal= {arXiv preprint arXiv:2001.11632},
year = {2020}
}
Comments
21pages