PreprintCC BY 4.0arXiv
On the Hasse principle for a block-diagonal form and a form of lower degree
Abstract
We investigate the Hasse principle for systems consisting of one form of degree k which decomposes as a sum of n-ary forms, and one general form of degree d < k. By exploiting the block structure of the first form before applying Weyl differencing, we refine the method of Brandes and Parsell (arXiv:2003.04350) in this setting; in particular, for a sum of binary quartic forms and a quadratic form, the requirement s > 516 is relaxed to s > 96, which also improves on the bound s > 100 available for general forms.
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BibTeX
@misc{johansson2026hasse,
title = {{On the Hasse principle for a block-diagonal form and a form of lower degree}},
author = {Anna Theorin Johansson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35639},
eprint = {2610.35639},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35639},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Hasse principle for a block-diagonal form and a form of lower degree
AU - Anna Theorin Johansson
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35639
UR - https://arxiv.org/abs/2610.35639
AB - We investigate the Hasse principle for systems consisting of one form of degree k which decomposes as a sum of n-ary forms, and one general form of degree d < k. By exploiting the block structure of the first form before applying Weyl differencing, we refine the method of Brandes and Parsell (arXiv:2003.04350) in this setting; in particular, for a sum of binary quartic forms and a quadratic form, the requirement s > 516 is relaxed to s > 96, which also improves on the bound s > 100 available for general forms.
ER -