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Kitaoka's conjecture for real cyclotomic fields
Abstract
We prove Kitaoka's conjecture for all real cyclotomic fields, i.e. for fields of the form ℚ(ζk+ζk−1) where ζk is a primitive kth root of unity. More precisely, we show that such a field admits a universal classical ternary quadratic form if and only if it is a real quadratic field.
Related
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BibTeX
@misc{krasensky2026kitaokas,
title = {{Kitaoka's conjecture for real cyclotomic fields}},
author = {Jakub Krásenský},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15109},
eprint = {2610.15109},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15109},
}
RIS
TY - UNPB
TI - Kitaoka's conjecture for real cyclotomic fields
AU - Jakub Krásenský
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15109
UR - https://arxiv.org/abs/2610.15109
AB - We prove Kitaoka's conjecture for all real cyclotomic fields, i.e. for fields of the form ℚ(ζ_k+ζ_k^−1) where ζ_k is a primitive kth root of unity. More precisely, we show that such a field admits a universal classical ternary quadratic form if and only if it is a real quadratic field.
ER -