James Punch

collaborators

5 papers

math.NT2026

Improved explicit Burgess-strength bounds for composite moduli

James Punch

Consider the character sum $S (M, N) = \sum_{n = M + 1}^{M + N} χ (n)$ for a non-principal Dirichlet character $χ (n)$ to a (possibly composite) modulus $q$ . Burgess proved that $S(M,N)\ll N^{1…

math.NT2025

Bounds on the Minkowski constants and a function involving $φ$

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

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

An improved upper bound on the covering radius of the logarithmic lattice of $Q (ζ_{n})$

James Punch

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

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…

Improved explicit Burgess-strength bounds for composite moduli

Bounds on the Minkowski constants and a function involving φ

The modified prime sieve for primitive elements in finite fields

An improved upper bound on the covering radius of the logarithmic lattice of Q(ζn​)

Quadratic units and cubic fields

Bounds on the Minkowski constants and a function involving $φ$

An improved upper bound on the covering radius of the logarithmic lattice of $Q (ζ_{n})$