S. Akhtari

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math.NT2026

A Classification of Multiply Monogenic Quartic Orders

Shabnam Akhtari, Jaxon Shumaker

We study two-times monogenic quartic orders; i.e., those of the shape $Z [α] = Z [β]$ , with algebraic integers $α$ and $β$ not $Z$ -equivalent. Two specific…

math.NT2025

Small integral generators of totally complex number fields

Shabnam Akhtari, Jeffrey Vaaler, Martin Widmer

Let $K$ be an algebraic number field and $H$ the absolute Weil height. Write $c_{K}$ for a certain positive constant that is an invariant of $K$ . We consider the question: does $K$ c…

math.NT2025

Effective equidistribution of norm one elements in CM-fields

Shabnam Akhtari, Jeffrey D. Vaaler, Martin Widmer

For a number field $K$ let $S_{K}$ be the maximal subgroup of the multiplicative group $K^{\times}$ that embeds into the unit circle under each embedding of $K$ into the comp…

math.NT2024

On rational points on classifying stacks and Malle's conjecture

Shabnam Akhtari, Jennifer Park, Marta Pieropan +1

In this expository article, we compare Malle's conjecture on counting number fields of bounded discriminant with recent conjectures of Ellenberg--Satriano--Zureick-Brown and Darda-…