Diophantine Approximation Festschrift for Wolfgang Schmidt
This volume contains 22 research and survey papers on recent developments in the field of diophantine approximation. The first article by Hans Peter Schlickewei is devoted to the scientific work of Wolfgang Schmidt. Further contributions deal with the sub
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Developments in Mathematics VOLUME 16
Series Editor: Krishnaswami Alladi, University of Florida, U.S.A.
Aims and Scope Developments in Mathematics is a book series publishing (i) (ii) (iii)
Proceedings of conferences dealing with the latest research advances, Research monographs, and Contributed volumes focusing on certain areas of special interest.
Editors of conference proceedings are urged to include a few survey papers for wider appeal. Research monographs, which could be used as texts or references for graduate level courses, would also be suitable for the series. Contributed volumes are those where various authors either write papers or chapters in an organized volume devoted to a topic of special/current interest or importance. A contributed volume could deal with a classical topic that is once again in the limelight owing to new developments.
DIOPHANTINE APPROXIMATION Festschrift for Wolfgang Schmidt Edited by HANS PETER SCHLICKEWEI Philipps-Universit~it Marburg, Marburg, Germany KLAUS SCHMIDT Universit~it Wien, Vienna, Austria ROBERT E TICHY Technische Universit~it Graz, Graz, Austria
SpringerWien NewYork
2000 Mathematics Subject Classification: liD, llJ, l l K This work is subject to copyright. All fights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machines or similar means, and storage in data banks. Product Liability: The publisher can give no guarantee for the information contained in this book. This also refers to that on drug dosage and application thereof. In each individual case the respective user must check the accuracy of the information given by consulting other pharmaceutical literature. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 9 2008 Springer-Verlag/Wien Printed in Germany SpringerWienNewYork is part of Springer Science+Business Media springer.at Typesetting: Scientific Publishing Services (P) Ltd., Chennai, India Printing: Strauss GmbH, Mrrlenbach, Germany Printed on acid-free and chlorine-free bleached paper SPIN 12102310 With 10 figures Library of Congress Control Number 2008930106
ISBN 978-3-211-74279-2 SpringerWienNewYork e-ISBN 978-3-211-74280-8 SpringerWienNewYork
CONTENTS Preface
vii
The mathematical work of Wolfgang Schmidt Hans Peter Schlickewei Sch~iffer's determinant argument Roger C. Baker
21
Arithmetic progressions and Tic-Tac-Toe games Jrzsef Beck
41
Metric discrepancy results for sequences {net} and Diophantine equations Istvdn Berkes, Walter Philipp, and Robert F. Tichy
95
Mahler's classification of numbers compared with Koksma's, II Yann Bugeaud
107
Rational approximations to a q-analogue of rt and some other q-series Peter Bundschuh and Wadim Zudilin
123
Orthogonality and digit shifts in the classical mean squares p
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