Number Theory A Seminar held at the Graduate School and University C
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1052 Number Theory A Seminar held at the Graduate School and University Center of the City University of NewYork 1982
Edited by D.V. Chudnovsky, G.V. Chudnovsky, H. Cohn and M. B. Nathanson I
I
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Editors
David V. Chudnovsky Gregory V. Chudnovsky Department of Mathematics, Columbia University NewYork, NY 10027, USA
Harvey Cohn Department of Mathematics, C.U.N.Y. City College NewYork, NY 10031, USA Melvyn B. Nathanson Department of Mathematics, Rutgers - The State University Newark, NJ 07102, USA
AMS Subject Classification (1980): 10-06 ISBN 3-54042909-X Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-38742909-X Springer-Verlag New York Heidelberg Berlin Tokyo Library of Congress Cataloging in Publication Data. Main entry under title: Number theory. (Lecture notes in mathematics; 1052) 1. Numbers, Theory of-Addresses, essays, lectures. I. Chudnovsky, D. (David), 1947-. II. NewYork Number Theory Seminar (1982-1983) III. Series: Lecture notes in mathematics (Springer-Verlag); 1052. QA3.L28 no. 1052 [QA241] 510s [512'.7] 84-1360 ISBN 0-387q2909-X (U.S.) This work is subject to copyright. All rights 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 machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich. © by Springer-Verlag Berlin Heidelberg 1984 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
INTRODUCT ION
In January, Chudnovsky,
1982 four number theorists
Harvey Cohn,
and Melvyn B. Nathanson
New York Number Theory Seminar. spring,
Manhattan.
The Seminar met weekly
during the
This volume
contains
expanded texts of the lectures
The Seminar
continued
academic year, and the reports presented be published
in a subsequent
The organizers Seminar will provide
Center
of New York at II West 42 Street in
delivered in the Seminar.
in the 1982-83
in this second year will
volume.
hope that the New York Number Theory a continuing
in the higher arithmetic,
the annual proceedings theory.
- organized the
1982 semester at the Graduate School and University
of the City University
results
- David and Gregory
opportunity
to discuss recent
and that the publication
will contribute
to research
of
in number
TABLE
OF
CONTENTS
K. A L L A D I , M o m e n t s o f A d d i t i v e F u n c t i o n s a n d S i e v e Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. C O H E N a n d H . W . L E N S T R A , JR. , H e u r i s t i c s o n C l a s s Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
D.V. C H U D N O V S K Y a n d G . V . C H U D N O V S K Y , Pad~ and Rational Approximations to Systems of Functions and their Arithmetic Applications . . . . . . . . . . . . . . . . . . . . . . .
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