A. Kobin

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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

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 $I ¨ $ -function - within a unif…

math.NT2025

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…

On p-adic solubility of Axℓ+Bym+Czn=0

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

Arithmetic Functions and Geometry

Categorifying Zeta Functions for Quadratic Covers

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