Gustav Kjaerbye Bagger

activity

20242026

collaborators

7 papers

math.NT2026

Determining norm-Euclidean complex cubic fields

Gustav Kjærbye Bagger, Andrew R. Booker, Tim Trudgian

We prove that Cavallar and Lemmermeyer's list of $58$ norm-Euclidean complex cubic fields is complete. The proof combines a classical discriminant bound with exact certificates of…

math.NT2026

Norm-Euclideanity in cyclic fields

Gustav Kjærbye Bagger

Consider a cyclic number field of prime degree $p$ . For a fixed degree, there are only finitely many such fields which are norm-Euclidean. When $p = 2$ or $3$ , these have been comple…

math.NT2026

Primitive normal progressions in finite fields

Gustav Kjærbye Bagger, Matthew Fernando

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 norm…

math.NT2026

A note on least primitive roots

Gustav Kjærbye Bagger

The least primitive root $g (p)$ modulo a prime $p$ is conjectured by Grosswald to satisfy $g (p) < p - 2$ for any $p > 409$ . We make progress towards the conjecture by proving $g(p…

math.NT2025

The modified prime sieve for primitive elements in finite fields

Gustav Kjærbye Bagger, James Punch

Let $r \geq 2$ be an integer, $q$ a prime power and $F_{q}$ the finite field with $q$ elements. Consider the problem of showing existence of primitive elements in a subset…

math.NT2025

The determination of norm-Euclidean cyclic cubic fields

Gustav Kjærbye Bagger, Andrew R. Booker, Bryce Kerr +3

It is known on the Generalised Riemann Hypothesis that there are precisely $13$ cyclic cubic fields that are norm-Euclidean. Unconditionally, there is a gap between analytic estima…

math.NT2024

Hybrid bounds for prime divisors

Gustav Kjærbye Bagger

Let $x$ and $n$ be positive integers. We prove a non-trivial lower bound for $x$ , dependant only on $ω_{n}$ , the number of distinct prime factors of $x^{n} - 1$ . By considering the divis…