John Yin

activity

20222026

collaborators

5 papers

math.NT2026

Counting Algebraic Integers of Bounded Height in Cyclotomic Fields

Phillip Harris, John Yin

In this note, we fix a height bound $B$ , and give a bound on the number of algebraic integers and units of absolute height at most $B$ in cyclotomic extensions $Q [ζ_{q}]$ , w…

math.NT2025

Counting points on some genus zero Shimura curves

Tyler Genao, Tristan Phillips, Fredderick Saia +2

We count certain abelian surfaces with potential quaternionic multiplication defined over a number field $K$ by counting points of bounded height on some genus zero Shimura curves.

math.NT2023

Counting Rational Points on the Stacky $Sym^{2} P^{1}$

John Yin

We prove the weak form of the generalized Batyrev-Manin-Malle conjecture formulated in \cite{ellenberg2021heights} for the stack $\operatorname{Sym}^2\mathbb{P}^1 := (\mathbb{P}^1…

math.NT2022

A Chebotarev Density Theorem over Local Fields

Asvin G, Yifan Wei, John Yin

We compute the $p$ -adic densities of points with a given splitting type along a (generically) finite map, analogous to the classical Chebotarev theorem over number fields and funct…

math.NT2022

Density of $p$ -adic polynomials generating extensions with fixed splitting type

John Yin

We prove that the density of polynomials $P (x) = \sum_{i = 0}^{n} a_{n} x^{n}$ over a local field $K$ generating an étale extension with specified splitting type is a rational function in te…

Counting Algebraic Integers of Bounded Height in Cyclotomic Fields

Counting points on some genus zero Shimura curves

Counting Rational Points on the Stacky Sym2P1

A Chebotarev Density Theorem over Local Fields

Density of p-adic polynomials generating extensions with fixed splitting type

Counting Rational Points on the Stacky $Sym^{2} P^{1}$

Density of $p$ -adic polynomials generating extensions with fixed splitting type