Several Complex Variables I Maryland 1970 Proceedings of the Interna
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Several Complex Variables I Maryland 1970
Proceedings of the International Mathematical Conference, held at College Park, April 6-17, 1970 Edited by John Horvath, University of Maryland, College Park, MD, USA
Springer-Verlag Berlin· Heidelberg· NewYork 1970
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is coucetned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 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' Heide1berg1970.Library ofCongress CatalogCardNumbet 72-137786 Printed in Germany. Tide No. 3312
PREFACE
The possibility of approaching major problems from diverse points of view is both a gratifying and significant aspect of mathematics.
With this in mind, an International Conference on Several
Complex Variables was organized and held at the University of Maryland, College Park, Maryland, from April 6 through 17, 1970.
This
volume (the first of two) contains some of the papers presented at this Conference.
Hopefully these reports, which represent the ideas
of many mathematicians working in distinct but related fields, will serve both mathematicians and mathematics. The Conference was supported in part by the Air Force Office of Scientific Research (contract number AFOSR70l83l) and the Office of Naval Research (contract number NOOOl467A023900l0).
CONTENTS
with
Baily, Walter L., Jr.
coefficients
Spaces of XLeinien
Bers, Lipman.
9
The
Bombieri, Enrico.
map of a compLex
35
of
88
methods in the
Eichler, M.
Grauert, Hans, and Riemenschneider, Oswald.
satae Raumen
anaLytische
auf kompLexen
Koranyi, Adam.
A compLex
on
Some
on On
Matsushima, Yozo.
domains
Narasimhan, Raghavan.
spaces
I. I.
Stoll, Wilhelm. Thimm, Walter.
Reduction of the fieLds of of functions on p-adic maniof
Extension of
maps anaLytic subsheaves
functions and
115 122
zeta functions
CohomoLogy with bounds on compLex
VaLue
Vesentini, Edoardo.
Banach
vaLues of functions of
and equivaLences of SiegeL
functions and the foLds
97 110
Residues on compLex spaces
Herrera, M.
Maass, H.
1
132 141
151 165 191
203
Further lectures given at the Conference
212
Further participants at the Conference
213
AUTOMORPHIC FORMS WITH INTEGRAL FOURIER COEFFICIENTS Walter L. Baily, Jr.
1
The purpose of this note is to prove that under aertain hypotheses, the graded ring of integral automorphic forms, with respect to an arithmetic group operating on a tube domain, is generated as a graded algebra over the complex numbers by a finite number of automorphic forms having rational integral Fourier coefficients.
The result, which seems to have some potential number-
theoretic interest, was inspired by notes of M. Eichler [8, esp. Satz 49] and by questions
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