English

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 ax2+bxy+cy2ax^2+bxy+cy^2. 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}
}

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21pages