Gustav Kjaerbye Bagger

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20242026

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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 KjÃ¦rbye 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 KjÃ¦rbye Bagger, Gustav Kjærbye Bagger, Andrew R. Booker +5

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 KjÃ¦rbye Bagger

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