Simon Myerson

Forms in many variables: an iterative approach

The circle method can be used to estimate the number of integral solutions of bounded size to a system of Diophantine equations, provided the number of variables is sufficiently large. When the equations are diagonal, such results typically rely on inductive arguments which repeatedly pass from the mean value of an exponential sum to the number of solutions to some system of equations and thence to a further mean value for a different exponential sum. I will discuss an approach of this type for non-diagonal equations.