6 papers · 1 filter
On -adic solubility of
Santiago Arango-Piñeros, Christopher Keyes, Andrew Kobin
We study -adic solubility of generalized Fermat equations for positive integers . For all but finitely many primes , the probability of…
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 that are defined using generalized Fermat equations, extend…
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 -function - within a unify…
Categorifying Zeta Functions for Quadratic Covers
Jon Aycock, Andrew Kobin
In various contexts, the zeta function of an object splits into a product of -functions. We categorify this product formula for quadratic covers of objects in the following cont…
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 -function of a quadratic Dirichlet character. We categorify this…
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…