On Waring's problem: some consequences of Golubeva's method

TL;DR

This paper explores advanced number theory problems related to sums of mixed powers, focusing on cases beyond traditional Hardy-Littlewood methods, and investigates consequences of Golubeva's approach.

Contribution

It introduces new results on Waring's problem for mixed powers using Golubeva's method, extending the scope beyond classical techniques.

Findings

Derived new bounds for sums involving mixed powers

Extended the applicability of Golubeva's method to complex cases

Identified limitations of Hardy-Littlewood method in certain scenarios

Abstract

We investigate sums of mixed powers involving two squares, two cubes, and various higher powers, concentrating on situations inaccessible to the Hardy-Littlewood method.