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

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

2004-06-22

arxiv.org/abs/math/0406434v1

Mathematics

Number Theory

Approx. 20 pages. Submitted to Journal of Number Theory

Scientific paper

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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