PreprintCC BY-NC-ND 4.0arXiv
Ternary Perfect Forms Over Imaginary Quadratic Field
Abstract
In this work, we enumerate the ternary perfect forms over all imaginary quadratic fields of absolute discriminant up to $91$ and study the number and combinatorial types of their associated polytopes. We prove a bound on the number of combinatorial types that can arise regardless of the discriminant. We analyze the data and make several observations concerning the number and complexity of the perfect forms that arise in the scope of our calculation.
Related
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BibTeX
@misc{parker2026ternary,
title = {{Ternary Perfect Forms Over Imaginary Quadratic Field}},
author = {Zachary Parker and Dan Yasaki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31479},
eprint = {2609.31479},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31479},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Ternary Perfect Forms Over Imaginary Quadratic Field
AU - Zachary Parker
AU - Dan Yasaki
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31479
UR - https://arxiv.org/abs/2609.31479
AB - In this work, we enumerate the ternary perfect forms over all imaginary quadratic fields of absolute discriminant up to $91$ and study the number and combinatorial types of their associated polytopes. We prove a bound on the number of combinatorial types that can arise regardless of the discriminant. We analyze the data and make several observations concerning the number and complexity of the perfect forms that arise in the scope of our calculation.
ER -