English

Integral Quadratic Forms Avoiding Arithmetic Progressions

Number Theory 2019-09-19 v1

Abstract

For every positive integer k, it is shown that there exists a positive definite diagonal quaternary integral quadratic form that represents all positive integers except for precisely those which lie in k arithmetic progressions. For k=1, all forms with this property are determined.

Keywords

Cite

@article{arxiv.1909.08561,
  title  = {Integral Quadratic Forms Avoiding Arithmetic Progressions},
  author = {A. G. Earnest and Ji Young Kim},
  journal= {arXiv preprint arXiv:1909.08561},
  year   = {2019}
}

Comments

8 pages