Phillip Harris

activity

20222026

collaborators

3 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.NT2024

Uniform bounds for maximal flat periods on $S L_{n} (R)$

Phillip Harris

Let $X$ be a compact locally symmetric space associated to $S L_{n} (R)$ and $Y \subset X$ a maximal flat submanifold, not necessarily closed. Using a Euclidean approximation,…

math.GR2022

Random Nilpotent Groups of Maximal Step

Phillip Harris

Let $G$ be a random torsion-free nilpotent group generated by two random words of length $ℓ$ in $U_{n} (Z)$ . Letting $ℓ$ grow as a function of $n$ , we analyze the step…

Counting Algebraic Integers of Bounded Height in Cyclotomic Fields

Uniform bounds for maximal flat periods on SLn​(R)

Random Nilpotent Groups of Maximal Step

Uniform bounds for maximal flat periods on $S L_{n} (R)$