On pairs of quadratic forms in five variables

TL;DR

This paper improves the upper bounds on the number of integral solutions of height for systems of two quadratic forms in five variables, advancing previous results by Iwaniec and Munshi.

Contribution

It provides a tighter upper bound for solutions to two quadratic forms in five variables, enhancing existing bounds in the literature.

Findings

Established a new upper bound for solutions of quadratic forms

Improved upon previous bounds by Iwaniec and Munshi

Contributed to the understanding of solutions to quadratic systems

Abstract

In this article, we obtain an upper bound for the number of integral solutions, of given height, of system of two quadratic forms in five variables. Our bound is an improvement over the bound given by Henryk Iwaniec and Ritabrata Munshi in \cite{H-R}.