Liam Baker

activity

20152026

collaborators

9 papers

math.RA2026

Prime-Power Multiplicative Modular Monoid Morphisms

Joseph Atalaye, Liam Baker, Sophie Marques

We undertake a systematic study of multiplicative monoid morphisms between prime-power modular monoids $(Z / p^{e} Z, \cdot)$ and $(Z / q^{f} Z, \cdot)$ , fo…

math.NT2026

On periods of the Tribonacci sequence modulo primes

Liam Baker, Florian Luca, Kerry Porrill

In this paper, we study the $p$ -adic zeros of the Tribonacci sequence $T_{n}$ , for a prime $p$ . In particular, we complete the analysis that was done in a 2024 paper of Yuri Bilu by…

math.RA2026

Direct-product rigidity and factor reconstruction for monoids with zero

Joseph Atalaye, Liam Baker, Sophie Marques

We study direct products of monoids with zero and give a criterion under which their factors can be recovered from the multiplicative structure alone. While classical decomposition…

math.NT2026

Drinfeld modular forms of higher rank from a lattice-oriented point of view

Liam Baker

A space $L_{N}^{r}$ of Drinfeld modules of rank $r \geq 1$ with level structure, or equivalently lattices of rank $r$ with level structure, is introduced, and its irreducible…

math.NT2026

Drinfeld modules in rank 2 with CM and S-unit j-invariants

Liam Baker, Fabien Pazuki, Patricio Perez Pina

We prove the finiteness of the set of $j$ -invariants of Drinfeld modules of rank 2 over $F_{q} [T]$ which are CM and $S$ -units, for $S$ the infinite set of primes with even d…

math.RA2026

Automorphism groups of direct products of multiplicative monoids of certain rings

Joseph Atalaye, Liam Baker, Sophie Marques

In this paper, we establish a rigidity result for automorphisms of multiplicative direct products of $D$ -rings which are total ring of fraction that have pairwise distinct cardinal…

math.NT2025

A parallelogram height inequality for Drinfeld modules

Liam Baker, Richard Griffon, Fabien Pazuki

We prove an inequality relating the Taguchi heights of four Drinfeld modules arranged in a ``parallelogram of isogenies''. This inequality is the analogue for Drinfeld modules of t…

math.RA2024

On the automorphism group of the monoid of the integers modulo a prime power

Joseph Atalaye, Liam Baker, Sophie Marques

This paper determines the structure of the automorphism group of the unit group $(U_{p^e}, \cdot)$ and the monoid $(\mathbb{Z}/p^e \mathbb{Z}, \cdot)$. For $ e \geq 5 $, we e…

math.NT2015

Erdős-Surányi sequences and trigonometric integrals

Liam Baker, Stephan Wagner

We study representations of integers as sums of the form $\pm a_{1} \pm a_{2} \pm \dots \pm a_{n}$ , where $a_{1}, a_{2}, \dots$ is a prescribed sequence of integers. Such a sequence is called…