Number Theory Carbondale 1979 Proceedings of the Southern Illinois N
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Number Theory Carbondale 1979 Proceedings of the Southern Illinois Number Theory Conference Carbondale, March 30 and 31, 1979
Edited by Melvyn B. Nathanson
Springer-Verlag Berlin Heidelberg New York 1979
Editor
Melvyn B. Nathanson Department of Mathematics Southern Illinois University at Carbondale Carbondale, IL 62901/USA
AMS Subject Classifications (1980): 10-06 ISBN 3-540-09559-4 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-09559-4 Springer-Verlag New York Heidelberg Berlin Library of Congress Cataloging in Publication Data Southern Illinois Number Theory Conference, Carbondale, Ill., 1979. Number theory, Carbondale 1979. (Lecture notes in mathamatics; 751) Bibliography: p. Includes index. 1. Numbers, Theory of--Congresses. I. Nathanson, Melvyn B., 1944· II. Title. Ill. Series: Lecture notes in mathematics (Berlin); 751. OA3.L28 no. 751 [OA241] 510'.8s [512'.7] 79-21887 ISBN 0·387·09559-4 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 the publisher, the amount of the fee to be determined by agreement with the publisher.
© by Springer-Verlag Berlin Heidelberg 1979 Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
PREFACE These are the proceedings of a conference on number theory held at Southern Illinois University at Carbondale on March 30 and 31, 1979.
For many years, number theorists in Illinois and nearby states
have gathered each fall and spring on a Saturday morning to discuss their recent results and work in progress.
The SIU meeting was an
enlarged version of this Illinois Number Theory Conference.
More
than 50 mathematicians came together in Carbondale for 28 lectures on diverse topics in analytic, algebraic, additive, and combinatorial number theory.
This volume contains expanded versions of many of
these talks, as well as papers contributed by H. Cohn and G. V. Chudnovsky, who were unable to attend. I am grateful to the Department of Mathematics at Southern Illinois University at Carbondale for providing financial support for the conference.
I wish to thank Sharon Champion for her excellent
typing of several of the papers in this volume.
Finally, I thank
all of the number theorists who came to Carbondale for their contributions to the success of the conference.
Melvyn B. Nathanson 29 June 1979
TABLE OF CONTENTS 1.
K. Alladi and M. L. Robinson, On certain irrational values of the logarithm.
2.
R.
3.
W. Dale Brownawell, On the development of Gelfand's method.
18
4.
G. V. Chudnovsky, Transcendental numbers
45
5.
Harvey Cohn, Diophantine equations over IT(t) and complex multiplication . .
70
6.
Gary Cornell, Abhyankar's lemma and the class group.
82
7.
Paul Erdos and M
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