No abstract

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.

No abstract

No abstract

In the following let Ω be the set of irrational numbers in the interval [0,1] and let λ be Lebesgue measure restricted to Ω. For any real number x, let {x} = x - [x] be the fractional part of x. Let N be anatural number and let α e Ω. Thenis known as the discrepancy of the sequence (nα)n>1 modulo 1; here c[x, y) denotes the characteristic function of the interval [x, y).