4 papers · 1 filter
Determining norm-Euclidean complex cubic fields
Gustav Kjærbye Bagger, Andrew R. Booker, Tim Trudgian
We prove that Cavallar and Lemmermeyer's list of norm-Euclidean complex cubic fields is complete. The proof combines a classical discriminant bound with exact certificates of…
Norm-Euclideanity in cyclic fields
Gustav Kjærbye Bagger
Consider a cyclic number field of prime degree . For a fixed degree, there are only finitely many such fields which are norm-Euclidean. When or , these have been comple…
Primitive normal progressions in finite fields
Gustav Kjærbye Bagger, Matthew Fernando
Consider an arithmetic progression inside the finite field . We study the existence of progressions whose terms are all primitive and at least one of them is norm…
A note on least primitive roots
Gustav Kjærbye Bagger
The least primitive root modulo a prime is conjectured by Grosswald to satisfy for any . We make progress towards the conjecture by proving $g(p…