D. Fretwell

activity

20162026

most citedInteracting Particle Systems and Jacobi Style Identities

3 citations · 3 across the 10 of their papers we have counts for

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11 papers · 1 filter

math.NT2026

Hecke modules associated to certain even ternary lattices of half-discriminant $N^{2}$

Samadrito Bhattacharyya, Giovanna De Lauri, Dan Fretwell

We consider Hecke modules of orthogonal modular forms attached to definite even ternary lattices of half-discriminant $N^{2}$ , where $N > 1$ is odd and square-free. We prove explicit…

math.NT2026

On smooth elements in arithmetic semigroups

Giovanna De Lauri, Dan Fretwell, Jack Ye

In this paper we explore the concept of smoothness in arithmetic semigroups. In particular, we give explicit asymptotics for the counting function $Ψ_{G} (x, y)$ when the arithmetic se…

math.NT2024

Hilbert modular Eisenstein congruences of local origin

Dan Fretwell, Jenny Roberts

Let $F$ be an arbitrary totally real field. Under weak conditions we prove the existence of certain Eisenstein congruences between parallel weight $k \geq 3$ Hilbert eigenforms of…

math.NT2023

On $2$ -superirreducible polynomials over finite fields

Jonathan W. Bober, Lara Du, Dan Fretwell +2

We investigate $k$ -superirreducible polynomials, by which we mean irreducible polynomials that remain irreducible under any polynomial substitution of positive degree at most $k$ .…

math.NT2023

Newform Eisenstein Congruences of Local Origin

Dan Fretwell, Jenny Roberts

We give a general conjecture concerning the existence of Eisenstein congruences between weight $k \geq 3$ newforms of square-free level $N M$ and weight $k$ new Eisenstein series of…

math.NT2022

Definite orthogonal modular forms: Computations, Excursions and Discoveries

Eran Assaf, Dan Fretwell, Colin Ingalls +3

We consider spaces of modular forms attached to definite orthogonal groups of low even rank and nontrivial level, equipped with Hecke operators defined by Kneser neighbours. After…

math.NT2020

Automorphic forms for some even unimodular lattices

Neil Dummigan, Dan Fretwell

We look at genera of even unimodular lattices of rank $12$ over the ring of integers of $Q (5)$ and of rank $8$ over the ring of integers of $Q (3)$ ,…

math.NT2019

Hecke operators on Hilbert-Siegel theta series

Dan Fretwell, Lynne Walling

We consider the action of Hecke-type operators on Hilbert-Siegel theta series attached to lattices of even rank. We show that average Hilbert-Siegel theta series are eigenforms for…

math.NT2017

Smooth values of polynomials

Jonathan Bober, Dan Fretwell, Greg Martin +1

Given $f \in Z [t]$ of positive degree, we investigate the existence of auxiliary polynomials $g \in Z [t]$ for which $f (g (t))$ factors as a product of polynomials of…

math.NT2016

Generic level $p$ Eisenstein congrunces for GSp $_{4}$

Dan Fretwell

We investigate level $p$ Eisenstein congruences for GSp $_{4}$ , generalisations of level $1$ congruences predicted by Harder. By studying the associated Galois and automorphic represe…