Exponential sums nondegenerate relative to a lattice

TL;DR

This paper improves bounds on exponential sums by introducing a systematic p-power reduction technique, addressing previous limitations when polynomial variables' powers are divisible by p.

Contribution

It introduces a new p-power reduction method that extends and strengthens earlier exponential sum results, especially in cases involving divisibility by p.

Findings

Enhanced bounds for exponential sums with p-power divisibility

Systematic p-power reduction technique developed

Broader applicability of previous theorems achieved

Abstract

Our previous theorems on exponential sums often did not apply or did not give sharp results when certain powers of a variable appearing in the polynomial were divisible by p. We remedy that defect in this paper by systematically applying "p-power reduction," making it possible to strengthen and extend our earlier results.