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.
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