A. Kobin

activity

20142026

collaborators

11 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.AG2025

Wild Stacky Curves and Rings of Mod p Modular Forms

Andrew Kobin, David Zureick-Brown

We extend work of Voight and the second author to compute the log canonical ring of a wild stacky curve over a field of characteristic $p > 0$ , which allows us to compute rings 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

Arithmetic Functions and Geometry

Andrew Kobin

In this expository note, we revisit several classical arithmetic functions - namely Euler's totient function, the divisor sum functions and Dedekind's $ψ$ -function - within a unify…

math.AG2023

Artin-Schreier-Witt Theory for Stacky Curves

Andrew Kobin

We extend our previous classification of stacky curves in positive characteristic using higher ramification data and Artin-Schreier-Witt theory. The main new technical tool introdu…

math.NT2023

Categorifying Zeta Functions for Quadratic Covers

Jon Aycock, Andrew Kobin

In various contexts, the zeta function of an object splits into a product of $L$ -functions. We categorify this product formula for quadratic covers of objects in the following cont…

math.NT2022

Categorifying quadratic zeta functions

Jon Aycock, Andrew Kobin

The Dedekind zeta function of a quadratic number field factors as a product of the Riemann zeta function and the $L$ -function of a quadratic Dirichlet character. We categorify this…

math.NT2020

A Primer on Zeta Functions and Decomposition Spaces

Andrew Kobin

Many examples of zeta functions in number theory and combinatorics are special cases of a construction in homotopy theory known as a decomposition space. This article aims to intro…

math.AG2019

$A^{1}$ -Local Degree via Stacks

Andrew Kobin, Libby Taylor

We extend results of Kass--Wickelgren to define an Euler class for a non-orientable (or non-relatively orientable) vector bundle on a smooth scheme, valued in the Grothendieck--Wit…

math.AG2019

Artin-Schreier Root Stacks

Andrew Kobin

We classify stacky curves in characteristic $p > 0$ with cyclic stabilizers of order $p$ using higher ramification data. This approach replaces the local root stack structure of a…

math.GT2014

Crossing Number Bound in Knot Mosaics

Hugh Howards, Andrew Kobin

Knot mosaics are used to model physical quantum states. The mosaic number of a knot is the smallest integer $m$ such that the knot can be represented as a knot $m$ -mosaic. In this…

On p-adic solubility of Axℓ+Bym+Czn=0

Wild Stacky Curves and Rings of Mod p Modular Forms

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

Arithmetic Functions and Geometry

Artin-Schreier-Witt Theory for Stacky Curves

Categorifying Zeta Functions for Quadratic Covers

Categorifying quadratic zeta functions

A Primer on Zeta Functions and Decomposition Spaces

A1-Local Degree via Stacks

Artin-Schreier Root Stacks

Crossing Number Bound in Knot Mosaics

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

$A^{1}$ -Local Degree via Stacks