Theta Functions
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Theta Functions
Springer-Verlag New York Heidelberg Berlin 1972
Jun-ichi 19usa The Johns Hopkins University, Baltimore. Md. 21218, USA
GeschiiftsfUbrende Herausgeber:
B.Eckmann Eidgeniissische Technische Hochschule ZUrich
B. L. van der Waerden Mathematisches Institut der U niversitiit ZUrich
AMS Subject Classifications (1970) Primary 14-XX, 13-XX, 32·XX Secondary 10-XX, ~2-XX, 43-XX, 81-XX
ISBN -13 :978-3-642-65317-9 DOl: 10.1007/978-3-642-65315-5
e-ISBN-13: 978-3-642-65315-5
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 iIIustrations. 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 Spr!nger-VerlagBeriinHeidelberg 1972. Softcover reprint of the hardcover 1st edition 1972 Library of Congress Catalog Card Number 74-183900.
Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Beriicksichtigung der Anwendungsgebiete Band 194
Herausgegeben von J. L. Doob . A. Grothendieck . E. Heinz· F. Hirzebruch E. Hopf . W. Maak . S. MacLane . W. Magnus· J. K. Moser D. Mumford· M. M. Postnikov· F. K. Schmidt· D. S. Scott K. Stein Geschiifts/iihrende Herausgeber B. Eckmann und B. L. van derWaerden
lun-ichi Igusa
Theta Functions
Springer-Verlag Berlin Heidelberg New York 1972
Jun-ichl 19usa The 10hns Hopkins University, Baltimore, Md. 21218, USA
Geschilftsfiihrende Herausgeber:
B.Eckmann EidgenOssische Technische Hochschule Zlirich
B. L. van der Waerden Mathematisches Institut der Universitiit Zlirich
AMS Subject Classifications (1970) Primary 14-XX, 13-XX, 32-XX Secondary 100XX, 22-XX, 43-XX, 81-XX
ISBN -13: 978-3-642-65317-9 e- ISBN -13: 978-3-642-65375-5 DOl: 10.1007/978-3-642-65375-5
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 1972. Library of Congress Catalog Card Number 74-183900. Softcover reprint of the hardcover 1st edition 1972
Foreword The theory of theta functions has a long history; for this, we refer the reader to an encyclopedia article by A. Krazer and W. Wirtinger ("Sources" [9]). We shall restrict ourselves to postwar, i.e., after 1945, periods. Around 1948/49, F. Conforto, c.L. Siegel, A. Well reconsidered the main existence theorems of theta functions and found natural proofs for them. These are contained in Conforto: Abe
