PreprintCC BY 4.0arXiv
Counting solutions to quadratic forms in eight prime variables of off-diagonal rank $3$
Abstract
In this note we count the number of solutions to a non-degenerate quadratic form in eight prime variables of off-diagonal rank $3$. It is a continuation of work by L. Zhao, who counted solutions to forms in at least nine variables, by B. Green, who counted solutions to 'generic' (which implies off-diagonal rank $4$) forms in eight variables, and by J. Dobrowolski, who counted solutions to forms in eight variables of off-diagonal rank at most $2$.
Related
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BibTeX
@misc{kowalska2026counting,
title = {{Counting solutions to quadratic forms in eight prime variables of off-diagonal rank $3$}},
author = {Aleksandra Kowalska},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30920},
eprint = {2608.30920},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30920},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Counting solutions to quadratic forms in eight prime variables of off-diagonal rank $3$
AU - Aleksandra Kowalska
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30920
UR - https://arxiv.org/abs/2608.30920
AB - In this note we count the number of solutions to a non-degenerate quadratic form in eight prime variables of off-diagonal rank $3$. It is a continuation of work by L. Zhao, who counted solutions to forms in at least nine variables, by B. Green, who counted solutions to 'generic' (which implies off-diagonal rank $4$) forms in eight variables, and by J. Dobrowolski, who counted solutions to forms in eight variables of off-diagonal rank at most $2$.
ER -