E. Mrema

collaborators

3 papers

math.CO2025

A study of a recursive sequence of polynomials revealing weighted Catalan Numbers

Sophie Marques, Elizabeth Mrema

This paper examines the recursive sequence of polynomials $p_{n} (x)$ , defined by $p_{0} (x) = x^{2} - 2$ and $p_{n} (x) = p_{n - 1} (x)^{2} - 2$ for $n \geq 1$ . It describes the field-theoretic m…

math.NT2024

A note on quadratic cyclotomic extensions

Sophie Marques, Elizabeth Mrema

This paper provides two characterizations of the primitive roots of unity in quadratic cyclotomic extensions over arbitrary fields. Firstly, we introduce a mapping from $\mathbb{N}…

math.NT2024

When is a 2-Power Cyclotomic Extension cyclic?

Sophie Marques, Elizabeth Mrema

This paper characterizes the cyclicity property of $2$ -power cyclotomic extensions through various means: the structure of the Galois groups, the nature of their subextensions, tow…