Leading lights in mathematics acknowledge the contribution of British mathematician, Klaus Roth, to number theory, diophantine approximation, sieve theory and beyond. Extensive lists of references make this a valuable source for research mathematicians in many areas and a suitable introductory overview of the subject for beginning research students.

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W. W. L. Chen is Emeritus Professor of Mathematics in the Department of Mathematics at Macquarie University, Sydney.

W. T. Gowers is Rouse Ball Professor of Mathematics in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge.

H. Halberstam is Professor Emeritus in the Department of Mathematics at the University of Illinois, Urbana-Champaign.

W. M. Schmidt is a Distinguished Professor Emeritus in the Department of Mathematics at the University of Colorado, Boulder.

R. C. Vaughan is Professor of Mathematics in the Department of Mathematics at Pennsylvania State University.

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