A Quaternionic Proof of the Representation Formula of a Quaternary Quadratic Form

Jesse I. Deutsch

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A Quaternionic Proof of the Representation Formula of a Quaternary Quadratic Form

Jesse I. Deutsch

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Abstract

Recently the author used certain quaternion orders to demonstrate the universality of some quaternary quadratic forms. Here a further study is done on one of these orders analogous to Hurwitz's proof of the formula for the number of representations of a positive integer by sums of four squares using quaternions. The result is the formula for the number of representations of a positive integer by one of the above mentioned quaternary quadratic forms.

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BibTeX RIS

Jesse I. Deutsch. 2004-06-22. A Quaternionic Proof of the Representation Formula of a Quaternary Quadratic Form. https://arxiv.org/abs/math/0406434

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