Number Theory and Related Fields In Memory of Alf van der Poorten

Number Theory and Related Fields collects contributions based on the proceedings of the “International Number Theory Conference in Memory of Alf van der Poorten,” hosted by CARMA and held March 12–16, 2012, at the University of Newcastle, Australia. The p

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Jonathan M. Borwein Igor Shparlinski Wadim Zudilin Editors

Number Theory and Related Fields In Memory of Alf van der Poorten

Springer Proceedings in Mathematics & Statistics Volume 43

For further volumes: http://www.springer.com/series/10533

Springer Proceedings in Mathematics & Statistics

This book series features volumes composed of select contributions from workshops and conferences in all areas of current research in mathematics and statistics, including OR and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematical and statistical research today.

Jonathan M. Borwein • Igor Shparlinski Wadim Zudilin Editors

Number Theory and Related Fields In Memory of Alf van der Poorten

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Editors Jonathan M. Borwein Centre for Computer Assisted Research Mathematics and its Applications School of Mathematical & Physical Sciences University of Newcastle Callaghan, NSW, Australia

Igor Shparlinski Department of Computing Macquarie University Sydney, NSW, Australia

Wadim Zudilin Centre for Computer Assisted Research Mathematics and its Applications School of Mathematical & Physical Sciences University of Newcastle Callaghan, NSW, Australia

ISSN 2194-1009 ISSN 2194-1017 (electronic) ISBN 978-1-4614-6641-3 ISBN 978-1-4614-6642-0 (eBook) DOI 10.1007/978-1-4614-6642-0 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013936399 © Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names ar