The Hardy–Littlewood circle method was invented a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is it capable of handling remarkably general systems of polynomial equations defined over arbitrary global fields, but it can also shed light on the spaces of rational curves that lie on suitable algebraic varieties.  This book, in which the arithmetic of cubic polynomials is centre stage, is aimed at bringing beginning graduate students into contact with some of the many facets of the circle method, both classical and modern.weiterlesen