Energy bounds, bilinear sums and their applications in function fields

TL;DR

This paper develops energy bounds in function fields, applies them to bilinear sums, and explores implications for smooth and square-free polynomials in residue classes, advancing understanding in algebraic number theory.

Contribution

It introduces new energy bounds in function fields and demonstrates their applications to bilinear sums and polynomial residue class problems.

Findings

Derived function field analogues of energy bounds for modular square roots and inversions.

Applied bounds to estimate bilinear sums in function fields.

Provided insights into the distribution of smooth and square-free polynomials in residue classes.

Abstract

We obtain function field analogues of recent energy bounds on modular square roots and modular inversions and apply them to bounding some bilinear sums and to some questions regarding smooth and square-free polynomials in residue classes.