English

Euclidean quadratic forms are ADC forms: A short proof

Number Theory 2016-09-23 v2

Abstract

This note presents a short, transparent proof of the theorem that every Euclidean quadratic form over a normed integral domain is an Aubry-Davenport-Cassels form. The theorem, as formulated in the note, allows besides quadratic terms also linear and constant terms, imposes no restrictions on the characteristic of the integral domain, and makes no unnecessary assumptions about the norm.

Keywords

Cite

@article{arxiv.1310.2093,
  title  = {Euclidean quadratic forms are ADC forms: A short proof},
  author = {France Dacar},
  journal= {arXiv preprint arXiv:1310.2093},
  year   = {2016}
}

Comments

Reformatted the typeset text (tighter line spacing etc). Improved a couple of formulations

R2 v1 2026-06-22T01:42:25.950Z