Evan M. O'Dorney

activity

20162026

most citedLarge orbits on Markoff-type K3 surfaces over finite fields

1 citations · 1 across the 13 of their papers we have counts for

collaborators

17 papers

math.NT2026

Galois groups of twisted reciprocal polynomials: a uniform asymptotic

Evan M. O'Dorney

We study the Galois group $G_{f}$ of a random polynomial $f$ in the family of polynomials of degree $2 n$ satisfying the twisted reciprocal relation $f (x) = x^{2 n} / b^{n} \cdot f (b / x)$ .…

math.NT2026

Galois groups of integer polynomials with prescribed coefficients

Evan M. O'Dorney

Fix a degree $n$ , a nonzero integer constant term, and some further coefficients of a monic integer polynomial, leaving $s$ coefficients to vary in $[- H, H]$ . We first prove that, w…

math.HO2026

Updating Tom Lehrer's "The Elements"

Evan M. O'Dorney

We analyze the poetico-comedic criteria by which Tom Lehrer arranged the chemical elements in his 1959 hit "The Elements," a parody to the tune of Gilbert and Sullivan's "The Moder…

math.NT2025

Galois groups of random integer matrices

Theresa C. Anderson, Evan M. O'Dorney

We study the number $M_{n} (T)$ be the number of integer $n \times n$ matrices $A$ with entries bounded in absolute value by $T$ such that the Galois group of characteristic polynomial…

math.NT2025

The structure of the double discriminant

Theresa C. Anderson, Ufuoma V. Asarhasa, Adam Bertelli +2

For a polynomial $f (x) = \sum_{i = 0}^{n} a_{i} x^{i}$ , we study the double discriminant $D D_{n, k} = disc_{a_{k}} disc_{x} f (x)$ . This object has been well studie…

math.NT2025

Étale algebras and the Kummer theory of finite Galois modules

Evan M. O'Dorney

Galois cohomology groups $H^{i} (K, M)$ are widely used in algebraic number theory, in such contexts as Selmer groups of elliptic curves, Brauer groups of fields, class field theory, a…

math.NT2024

Raney Transducers and the Lowest Point of the $p$ -Lagrange spectrum

Brandon Dong, Soren Dupont, Evan M. O'Dorney +1

It is well known that the golden ratio $ϕ$ is the ''most irrational'' number in the sense that its best rational approximations $s / t$ have error $\sim 1/ (5 t^{2})$ and this co…

math.NT2024

Galois groups of reciprocal polynomials and the van der Waerden-Bhargava theorem

Theresa C. Anderson, Adam Bertelli, Evan M. O'Dorney

We study the Galois groups $G_{f}$ of degree $2 n$ reciprocal (a.k.a. palindromic) polynomials $f$ of height at most $H$ , finding that $G_{f}$ falls short of the maximal possible group…

math.AG2024

Even-carry polynomials and cohomology of line bundles on the incidence correspondence in positive characteristic

Evan M. O'Dorney

We consider the cohomology groups of line bundles $L$ on the \emph{incidence correspondence}, that is, a general hypersurface $X \subset \mathbb{P}^{n-1} \times \mathbb{P…

math.NT2023

Section Rings of $Q$ -Divisors on Genus $1$ Curves

Michael Cerchia, Jesse Franklin, Evan O'Dorney

We compute generators and relations for the section ring of a rational divisor on an elliptic curve. Our technique generalizes the work of O'Dorney (in genus zero) and Voight--Zure…

math.NT2023

Renaissance canons with asymmetric schemes

Evan M. O'Dorney

By a "scheme" of a musical canon, we mean the time and pitch displacement of each entering voice. When the time displacements are unequal, achieving consonant sonorities is especia…

math.NT2022★ 1 cited

Large orbits on Markoff-type K3 surfaces over finite fields

Evan M. O'Dorney

We study the surface $W_{k} : x^{2} + y^{2} + z^{2} + x^{2} y^{2} z^{2} = k x y z$ in $(P^{1})^{3}$ , a tri-involutive K3 (TIK3) surface. We explain a phenomenon noticed by Fuchs,…

math.NT2022

Diophantine approximation on conics

Evan M. O'Dorney

Given a conic $C$ over $Q$ , it is natural to ask what real points on $C$ are most difficult to approximate by rational points of low height. For the an…

math.NT2022

Reflection theorems of Ohno-Nakagawa type for quartic rings and pairs of $n$ -ary quadratic forms

Evan M. O'Dorney

We prove a reflection theorem, conjectured by Nakagawa and Ohno, for the number of quartic rings, or pairs of ternary quadratic forms, with a given cubic resolvent. Over $\mathbb{Z…

math.NT2021

Composed varieties and reflection theorems of Ohno-Nakagawa type

Evan M. O'Dorney

The Ohno-Nakagawa (O-N) reflection theorem is an unexpectedly simple identity relating the number of $GL_{2} Z$ -classes of binary cubic forms (equivalently, cubic r…

math.NT2021

Reflection theorems for number rings

Evan M. O'Dorney

This is the original version of my Ph.D. thesis. The main results have been divided up between papers arXiv:2111.09784 and arXiv:2204.10924. This paper has been kept on the arXiv t…

math.NT2016

A remarkable identity in class numbers of cubic rings

Evan M. O'Dorney

In 1997, Y. Ohno empirically stumbled on an astoundingly simple identity relating the number of cubic rings $h (D)$ of a given discriminant $D$ , over the integers, to the number of…

Galois groups of twisted reciprocal polynomials: a uniform asymptotic

Galois groups of integer polynomials with prescribed coefficients

Updating Tom Lehrer's "The Elements"

Galois groups of random integer matrices

The structure of the double discriminant

Étale algebras and the Kummer theory of finite Galois modules

Raney Transducers and the Lowest Point of the p-Lagrange spectrum

Galois groups of reciprocal polynomials and the van der Waerden-Bhargava theorem

Even-carry polynomials and cohomology of line bundles on the incidence correspondence in positive characteristic

Section Rings of Q-Divisors on Genus 1 Curves

Renaissance canons with asymmetric schemes

Large orbits on Markoff-type K3 surfaces over finite fields

Diophantine approximation on conics

Reflection theorems of Ohno-Nakagawa type for quartic rings and pairs of n-ary quadratic forms

Composed varieties and reflection theorems of Ohno-Nakagawa type

Reflection theorems for number rings

A remarkable identity in class numbers of cubic rings

Raney Transducers and the Lowest Point of the $p$ -Lagrange spectrum

Section Rings of $Q$ -Divisors on Genus $1$ Curves

Reflection theorems of Ohno-Nakagawa type for quartic rings and pairs of $n$ -ary quadratic forms