English

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