Self-Reciprocal Polynomials and Coterm Polynomials

TL;DR

This paper classifies all self-reciprocal polynomials derived from reversed Dickson polynomials over integers and finite fields, and explores related coterm polynomials, providing a comprehensive understanding of their structure.

Contribution

It provides a complete classification of self-reciprocal polynomials from reversed Dickson polynomials and introduces coterm polynomials related to these structures.

Findings

All self-reciprocal polynomials from reversed Dickson polynomials are classified.

New coterm polynomials arising from reversed Dickson polynomials are identified.

The classification applies over both integers and finite fields.

Abstract

We classify all self-reciprocal polynomials arising from reversed Dickson polynomials over $\mathbb{Z}$ and $\mathbb{F}_p$, where $p$ is prime. As a consequence, we also obtain coterm polynomials arising from reversed Dickson polynomials.