Professor Hua Loo Keng in Japan

It is a great honour and pleasure for me to be invited to this International Symposium on Number Theory and Analysis dedicated to the memory of the late Professor Hua Loo Keng and to be given an opportunity to give a talk before you. Personally, I wonder

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umber Theory

Gong Sheng Lu Qi-keng Wang Yuan Yang Lo (Eds.)

International Symposium in Memory of Hua LooKeng Volume I Number Theory

Springer-Verlag Berlin Beideiberg GmbH

Gong Sheng Lu Qi-keng Wang Yuan Yang Lo (Eds.)

This proceedings volwne seroes as the 21st Vo/wne in the series in Pure and Ajplied Mathematics published by Science Press, Beijing, China.

Mathematics Subject Classification (1980): IOBXX IOCXX IOGXX

ISBN 978-3-662-07983-6 ISBN 978-3-662-07981-2 (eBook) DOI 10.1007/978-3-662-07981-2

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concemed, specifically the rights oftranslation, reprinting, re-use ofillustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication ofthis publication or parts thereofis only permitted under the provisions of the German Copyright Law of Septern her 9, 1965, in its current version and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.

© Springer-Verlag Berlin Beideiberg 1991 Originally published by Springer-Verlag Berlin Beideiberg New York in 1991 Softcoverreprint ofthe bardeover Istedition 1991

41;3140-543210

Preface

The international symposium on number theory and analysis in memory of the late famous Chinese mathematician Prof. Hua Loo Keng was co-sponsored by the Institute of Mathematics, Academia Sinica and the University of Science and Technology of China. lt took place between August Ist and 7th of 1988 on the campus of Tsing Hua University, and some 150 mathematicians were present. The symposium was carried out in two separate sections: number theory and analysis. This is retlected in the publication ofa set oftwo volumes, the first one on Number Theory edited by Professor Wang Yuan and the second on Analysis by Professors Gong Sheng, Lu Qi-keng and Yang Lo. The distinguished list of main speakers and the contents of these two volumes reflect the high level of the mathematical activity throughout the seven days. W e pay special tribute to our main speakers professors Chuang, Conn, Ding, Drasin, Fitzgerald, Gaier, Gong, Grauert, Gu, Hejhal, Iyanaga, Karatsuba, Koranyi, Liao, Lu, Pan, Richert, Satake, Schmidt, Siu, Tatuzawa, Tsang, Vladimirov, Y. Wang, G. Y. Wang, Wüstholz and Yang, who gave the excellent one hour lectures, and also to the participants who gave contributed talks on their own research work. The discussions among the mathematicians were always in a warm atmosphere. Our thanks go to professors Chern, Subbarao and Yau for their contributions to these proceedings. W e wish to express our thanks to the following institutions for their generous financial support: The Division of Mathematics, Physics and Chemistry of Academia Sinica, the University of Science and Technology of China, the Institute of Mathematics, Academia Sinica, and the Chinese National Natural Science Foundation. We also received support from the Third World Academy of Sciences for the international trave