A paucity problem for certain triples of diagonal equations

TL;DR

This paper addresses a specific scarcity problem for solutions to certain linked diagonal equations in ten variables, providing an asymptotic count of solutions using advanced mathematical techniques.

Contribution

It introduces a novel complification method to derive an asymptotic formula for solutions to complex diagonal equations, resolving a longstanding paucity problem.

Findings

Established an asymptotic formula for solutions

Resolved the paucity problem for the system

Demonstrated the effectiveness of complification techniques

Abstract

We consider certain systems of three linked simultaneous diagonal equations in ten variables with total degree exceeding five. By means of a complification argument, we obtain an asymptotic formula for the number of integral solutions of this system of bounded height that resolves the associated paucity problem.