Library of Congress CataIoging-in-Publication Data Hlawka, Edmund.[Geometrische und analytische Zahlentheorie. English) Geometric and analytic number theory/Edmund Hlawka, 10hannes SchoiBengeier, Rudolf Taschner. p. cm. -(Universitext) Translation of: Geometrische und analytische Zahlentheorie. Includes bibliographical references and index.

An Inequality of van der Corput and Kemperman. The tool of van der Corput's difference theorem in the theory of uniform distribution is his so-called fundamental inequality. KEMPERMAN showed that even the non-constructive proofs of the difference theorem by BASS, BERTRANDIAS and CIGLER implicitly use a more general form of van der Corput's fundamental inequality. In this article, the inequality which constitutes the basis of the difference theorem will be proved under a very general setting, applications will be demonstrated in connection with the uniform distribution of products of linear forms and a quantitative version of the difference theorem, i. e. an estimation of discrepancies, will be derived.10" 0026--9255/81/0091/0139/$02.80

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