A Quaternionic Proof of the Representation Formula of a Quaternary Quadratic Form
Number Theory
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0406434,
title = {A Quaternionic Proof of the Representation Formula of a Quaternary Quadratic Form},
author = {Jesse I. Deutsch},
journal= {arXiv preprint arXiv:math/0406434},
year = {2007}
}
Comments
Approx. 20 pages. Submitted to Journal of Number Theory