James Punch

collaborators

4 papers

math.NT2025

Bounds on the Minkowski constants and a function involving $I ¨ $

Giulia Pelizzari, James Punch

In 1887, Minkowski determined the least common multiple of the orders of all finite subgroups of $G L_{n} (Q)$ ; we refer to this number as $M (n)$ . In (Katznelson, 1994), Katzn…

math.NT2025

Quadratic units and cubic fields

Florian Breuer, James Punch

We investigate Eisenstein discriminants, which are squarefree integers $d \equiv 5 (mod 8)$ such that the fundamental unit $ε_{d}$ of the real quadratic field $K=\mathbb{Q…

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

An improved upper bound on the covering radius of the logarithmic lattice of $Q (I^¶_{n})$

James Punch

Let $R^{m}$ be endowed with the Euclidean metric. The covering radius of a lattice $I^ \subset R^{m}$ is the least distance $r$ such that, given any point of $\mathbb{…

Bounds on the Minkowski constants and a function involving I¨

Quadratic units and cubic fields

The modified prime sieve for primitive elements in finite fields

An improved upper bound on the covering radius of the logarithmic lattice of Q(I^¶n​)

Bounds on the Minkowski constants and a function involving $I ¨ $

An improved upper bound on the covering radius of the logarithmic lattice of $Q (I^¶_{n})$