Phillip Harris

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20222026

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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,…

Counting Algebraic Integers of Bounded Height in Cyclotomic Fields

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

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