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arXiv · 1610.09541

Integral matrices as diagonal quadratic forms

Jungin Lee
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Abstract

In this paper, we investigate the conditions under which a diagonal quadratic form $\sum_{i=1}^{m}a_i X_i^2$ represents every $n \times n$ integral matrix, where $a_i$ ($1 \leq i \leq m$) are integers. For $n=2$, we give a necessary and sufficient condition. Also we give some sufficient conditions for each $n \geq 2$ where $a_i$ ($1 \leq i \leq m$) are pairwisely coprime.

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Jungin Lee. 2016-10-29. Integral matrices as diagonal quadratic forms. https://doi.org/10.1080/03081087.2017.1320965

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