Pankaj Vishe: Introduction to the Circle method

We give an introduction to the famous Hardy Littlewood circle
method with its application to the Waring's problem. In particular, we
use the circle method to give asymptotics for the number of integral
solutions for a diagonal form with integer coefficients in ''large
enough'' variables (e.g., all sufficiently large integers are
represented as sums of ''enough'' k-th powers.)