New extensions to the sumsets with polynomial restrictions

TL;DR

This paper introduces new polynomial coefficients derived from the Morris identity's leading terms, enabling novel results in sumsets with polynomial restrictions using Alon's polynomial method.

Contribution

It develops new polynomial coefficients from the Morris identity's leading terms, advancing the study of sumsets with polynomial restrictions.

Findings

New polynomial coefficients obtained from Morris identity

Results improve understanding of sumsets with polynomial restrictions

Application of Alon's polynomial method to new coefficients

Abstract

By taking the leading and the second leading coefficients of the Morris identity, we get new polynomial coefficients. These coefficients lead to new results in the sumsets with polynomial restrictions by the polynomial method of N. Alon.