Ternary quadratic forms representing same integers
Number Theory
2020-04-07 v2
Abstract
In 1997, Kaplansky conjectured that if two positive definite ternary quadratic forms with integer coefficients have perfectly identical integral representations, then they are isometric, both regular, or included either of two families of ternary quadratic forms. In this article, we prove the existence of pairs of ternary quadratic forms representing same integers which are not in the Kaplansky's list.
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Cite
@article{arxiv.2002.02205,
title = {Ternary quadratic forms representing same integers},
author = {Jangwon Ju},
journal= {arXiv preprint arXiv:2002.02205},
year = {2020}
}
Comments
6 pages