Abstract
The most important analytic method for handling equidistribution questions about rational points on algebraic varieties is undoubtedly the HardyLittlewood circle method. There are a number of good texts available on the circle method, but the reader may particularly wish to study the books by Davenport [4] and Vaughan [11]. In this lecture we shall consider an irreducible form F (X1, . . . , Xn) ∈ Z[X1, . . . , Xn] of degree d which defines a hypersurface F = 0 in Pn−1. The fundamental questions will be: are there any rational points on the hypersurface? If so, are they equidistributed in a suitable sense? We shall address these issues by looking at integer points on the affine cone. Thus to ask about equidistribution with respect to measures on Pn−1(R), for example, we may take a small box R := n ∏
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