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arXiv · 2001.11632

Integers of the Form $ax^2+bxy+cy^2$

Naoki Uchida
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Abstract

We provide a characterization of integers represented by the positive definite binary quadratic form $ax^2+bxy+cy^2$. 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.

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Naoki Uchida. 2020-01-31. Integers of the Form $ax^2+bxy+cy^2$. https://arxiv.org/abs/2001.11632

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