Citlali Rocha-Ruiz

She/her

Education: Bachelor of Arts in mathematics

Mentor: Kim Klinger-Logan, Ph.D.

McNair Project: Counting Interior Roots

This research is focused on the roots of the polynomial f {n,k}(z) = zn + zk -1 with 0 < k < n.
Previous research shows that roots of the polynomial cluster around roots of unity on the unit
circle. An explicit formula for the roots of f {n,k} on the unit circle, which are called unimodular
roots, was previously given and the authors of this formula state many open problems related to
these roots. One such problem is related to the number of unimodular roots for a family F n of all
f {n,k} with 0 < k < n. In a recently submitted paper, an explicit formula for the number of
unimodular roots for a family F n has been given. With formulas for the roots of f {n,k} inside the
unit circle also given, we find a formula for the number of interior roots for a family F n of all
f {n,k} with 0 < k < n.