Arithmetic of Lucas Atoms: A Cyclotomic Perspective on Polynomial Recurrence Sequences

Specialeforsvar ved Carlos Reinaldo Mendes 

Titel: Arithmetic of Lucas Atoms: A Cyclotomic Perspective on Polynomial Recurrence Sequences

Abstract: The factorization of $x^n-1$ into cyclotomic polynomials is one of the classical links between algebra and number theory. In this talk, we present a related factorization theory arising from Lucas polynomial sequences through their primitive factors, known as Lucas atoms.
We begin by studying the arithmetic properties of these polynomials, then develop analogous cyclotomic constructions in other settings, including rational trigonometry. Finally, we discuss how these ideas extend beyond Lucas sequences, highlighting broader algebraic structures underlying polynomial recurrence systems.

Vejleder: Fabien Pazuki