On certain quaternary quadratic forms

Kazuhide Matsuda

On certain quaternary quadratic forms

Number Theory 2014-11-26 v1

Authors: Kazuhide Matsuda

Abstract

In this paper, we determine all the positive integers $a, b$ and $c$ such that every nonnegative integer can be represented as $f^{a,b}_c(x,y,z,w)=ax^2+by^2+c(z^2+zw+w^2) \,\, \textrm{with} \,\,x,y,z,w\in\mathbb{Z}.$ Furthermore, we prove that $f^{a,b}_c$ can represent all the nonnegative integers if it represents $n=1,2,3,5,6,10.$

Keywords

number theory quadratic forms

Cite

@article{arxiv.1411.6963,
  title  = {On certain quaternary quadratic forms},
  author = {Kazuhide Matsuda},
  journal= {arXiv preprint arXiv:1411.6963},
  year   = {2014}
}

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