Number Theory A Seminar held at the Graduate School and University C
The New York Number Theory Seminar was organized in 1982 to provide a forum for the presentation and discussion of recent advances in higher arithmetic and its applications. Papers included in this volume are based on the lectures presented by their autho
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1383 0.\1. Chudnovsky G.\I. Chudnovsky H. Cohn M.B. Nathanson (Eds.)
Number Theory A Seminar held at the Graduate School and University Center of the City University of New York 1985-88
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong
Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann
1383 0.\1. Chudnovsky G.\I. Chudnovsky H. Cohn M.B. Nathanson (Eds.)
Number Theory A Seminar held at the Graduate School and University Center of the City University of New York 1985-88
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong
Editors David V. Chudnovsky Gregory V. Chudnovsky Department of Mathematics, Columbia University New York, NY 10027, USA Harvey Cohn Department of Mathematics, (CUNY), City College New York, NY 10031, USA Melvyn B, Nathanson Provost and Vice President for Academic Affairs Lehman College (CUNY) Bronx, NY 10468, USA
Mathematics Subject Classification (1980): 10-06 ISBN 3-540-51549-6 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-51549-6 Springer-Verlag New York Berlin Heidelberg
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INTRODUCTION Th is is the fourth vo I ume of papers presented at the New York Number Theory Seminar. Since 1982 the Seminar has been meeting every Tuesday afternoon during the academic year at the Graduate School and University Center of the City University of New York. The goa 1 of the Sem i nar is to prov i de a forum for the exposure of new results in number theory and al lied fields in the New York metropolitan area. Mathematicians who plan to be in New York and wou 1d 1 ike to attend or 1ecture in the Sem i nar are encouraged to contact the organizers.
TABLE OF CONTENTS D. BUMP. J. HOFFSTEIN. Some Conjectured Relationships Between Theta Functions and Eisenstein Series on the Metaplectic Group . . . . • . . . . . . . . • . . . • . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . O.V. CHUONOVSKY. G.V. CHUONOVSKY. Computational 8roblems in Arithmetic of Linear Differential Equations. Some Diophantine App I i cat ions. . . . . • . . . . . . . . . . . • . . . . . . . . . . • . . . . . . . . • . . . . . .
12
H. COHN. Iteration
50
of Two-Valued Modular Equations .....
D. GOSS. Report on Transcendency in the Theory of Function Fields ..•.•••••..•••..•.•...........•••..••..•.•.•....•.
59
O. HAJELA. Exponential Su
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