PreprintarXiv licencearXiv
Primitive normal progressions in finite fields
Abstract
Consider an arithmetic progression inside the finite field 𝔽qn. We study the existence of progressions whose terms are all primitive and at least one of them is normal. Using a combination of sieve estimates, ramified bounds, and computational arguments, we improve significantly upon previous literature for progressions of length m=4 and obtain partial results whenever 5≤ m≤ 10. Finally, we provide a general bound which outperforms previous results in the range m≥ 53.
Related
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BibTeX
@misc{bagger2026primitive,
title = {{Primitive normal progressions in finite fields}},
author = {Gustav Kjærbye Bagger and Matthew Fernando},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07538},
eprint = {2610.07538},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07538},
}
RIS
TY - UNPB
TI - Primitive normal progressions in finite fields
AU - Gustav Kjærbye Bagger
AU - Matthew Fernando
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07538
UR - https://arxiv.org/abs/2610.07538
AB - Consider an arithmetic progression inside the finite field 𝔽_q^n. We study the existence of progressions whose terms are all primitive and at least one of them is normal. Using a combination of sieve estimates, ramified bounds, and computational arguments, we improve significantly upon previous literature for progressions of length m=4 and obtain partial results whenever 5≤ m≤ 10. Finally, we provide a general bound which outperforms previous results in the range m≥ 53.
ER -