Diophantine Inequalities (London Mathematical Society Monographs, 1)

This book launches the prestigious new series London Mathematical Society Monographs. The author, noted for his work throughout the mathematical community, here presents an overview of the theory of nonlinear Diophantine approximation. He has concentrated on the important progress made in the last ten years by such contributors as I. M. Vinogradov, H. Heilbronn, and W. M. Schmidt, finding, for example, that it is possible to consider simultaneous approximation to integers by values of a set of quadratic forms, or a discrete analogue (small solutions of a system of homogeneous congruences). Starting with the work of I.M. Vinogradov and H. Heilbronn, the author develops the theme of nonlinear Diophantine approximation in a number of different directions.