On pairs of quadratic forms in five variables

Abstract

In this paper, 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 in [H. Iwaniec and R. Munshi, The circle method and pairs of quadratic forms, J. Théor. Nr. Bordx. 22 (2010) 403–419].