C. Keyes

activity

20192026

most citedBounding the number of arithmetical structures on graphs

6 citations · 10 across the 9 of their papers we have counts for

collaborators

9 papers

math.NT2026

On $p$ -adic solubility of $A x^{ℓ} + B y^{m} + C z^{n} = 0$

Santiago Arango-Piñeros, Christopher Keyes, Andrew Kobin

We study $p$ -adic solubility of generalized Fermat equations $A x^{ℓ} + B y^{m} + C z^{n} = 0$ for positive integers $ℓ, m, n$ . For all but finitely many primes $p$ , the probability of…

math.NT2025

The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations

Juanita Duque-Rosero, Christopher Keyes, Andrew Kobin +3

We characterize the integral Hasse principle for an infinite family of spherical stacky curves with genus $g \in [2/3, 1)$ that are defined using generalized Fermat equations, extend…

math.NT2025

Effective Bertini theorems and zeros of $p$ -adic forms of degrees 7 and 11

Lea Beneish, Christopher Keyes

We establish an effective Bertini-type theorem for hypersurfaces $X_{f} : f = 0$ defined over a finite field $k$ for which $f$ has no linear factors over the algebraic closure $…

math.NT2024

How often does a cubic hypersurface have a rational point?

Lea Beneish, Christopher Keyes

A cubic hypersurface in $P^{n}$ defined over $Q$ is given by the vanishing locus of a cubic form $f$ in $n + 1$ variables. It is conjectured that when $n \geq 4$ , suc…

math.NT2021★ 2 cited

On the proportion of locally soluble superelliptic curves

Lea Beneish, Christopher Keyes

We investigate the proportion of superelliptic curves that have a $Q_{p}$ point for every place $p$ of $Q$ . We show that this proportion is positive and given by th…

math.NT2021★ 1 cited

Mertens' theorem for Chebotarev sets

Santiago Arango-Piñeros, Daniel Keliher, Christopher Keyes

We generalize Mertens' product theorem to Chebotarev sets of prime ideals in Galois extensions of number fields. Using work of Rosen, we extend an argument of Williams from cycloto…

math.NT2021

Fields generated by points on superelliptic curves

Lea Beneish, Christopher Keyes

We give an asymptotic lower bound on the number of field extensions generated by algebraic points on superelliptic curves over $Q$ with fixed degree $n$ and discriminant b…

math.CO2020★ 6 cited

Bounding the number of arithmetical structures on graphs

Christopher Keyes, Tomer Reiter

Let $G$ be a connected undirected graph on $n$ vertices with no loops but possibly multiedges. Given an arithmetical structure $(r, d)$ on $G$ , we describe a cons…

math.NT2019★ 1 cited

Growth of points on hyperelliptic curves

Christopher Keyes

Fix a hyperelliptic curve $C / Q$ of genus $g$ , and consider the number fields $K / Q$ generated by the algebraic points of $C$ . In this paper, we study the number of…

On p-adic solubility of Axℓ+Bym+Czn=0

The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations

Effective Bertini theorems and zeros of p-adic forms of degrees 7 and 11

How often does a cubic hypersurface have a rational point?

On the proportion of locally soluble superelliptic curves

Mertens' theorem for Chebotarev sets

Fields generated by points on superelliptic curves

Bounding the number of arithmetical structures on graphs

Growth of points on hyperelliptic curves

On $p$ -adic solubility of $A x^{ℓ} + B y^{m} + C z^{n} = 0$

Effective Bertini theorems and zeros of $p$ -adic forms of degrees 7 and 11