10 citations · 23 across the 17 of their papers we have counts for
26 papers
A Classification of Multiply Monogenic Quartic Orders
Shabnam Akhtari, Jaxon Shumaker
We study two-times monogenic quartic orders; i.e., those of the shape , with algebraic integers and not -equivalent. Two specific…
Effective equidistribution of norm one elements in CM-fields
Shabnam Akhtari, Jeffrey D. Vaaler, Martin Widmer
For a number field let be the maximal subgroup of the multiplicative group that embeds into the unit circle under each embedding of into the comp…
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-…
Small integral generators of totally complex number fields
Shabnam Akhtari, Jeffrey Vaaler, Martin Widmer
Let be an algebraic number field and the absolute Weil height. Write for a certain positive constant that is an invariant of . We consider the question: does c…
Quartic Index Form Equations and Monogenizations of Quartic Orders
Shabnam Akhtari
Some upper bounds for the number of monogenizations of quartic orders are established by considering certain classical Diophantine equations, namely index form equations in quartic…
Lower Bounds for Regulators of Number Fields in terms of their Discriminants
Shabnam Akhtari, Jeffrey D. Vaaler
We prove inequalities that compare the regulator of a number field with its absolute discriminant. We refine some ideas in Silverman's work in 1984 where such general inequalities…