English

A Universal Quaternary Quadratic Form over Gaussian Integers

Number Theory 2014-05-12 v2

Abstract

In this article we show that the form x2+iy2+z2+iw2x^2 + iy^2 + z^2 + iw^2 represents all gaussian integers. The main tools used in this proof are Fermat's little theorem (over finite field extensions), the Mordell-Niven theorem (representation of some gaussians), and the generalized Euler-identity over finite field extensions.

Keywords

Cite

@article{arxiv.1310.6293,
  title  = {A Universal Quaternary Quadratic Form over Gaussian Integers},
  author = {Felix Sidokhine},
  journal= {arXiv preprint arXiv:1310.6293},
  year   = {2014}
}
R2 v1 2026-06-22T01:52:38.004Z