Elliptic Modular Functions An Introduction

This book is a fully detailed introduction to the theory of modular functions of a single variable. I hope that it will fill gaps which in view ofthe lively development ofthis theory have often been an obstacle to the students' progress. The study of the

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Herausgegeben von

S. S. ehern J. L. Doob J. Douglas, jr. A. Grothendieek E. Heinz F. Hirzebrueh E. Hopf W. Maak S. MaeLane W. Magnus M. M. Postnikov F. K. Sehmidt D. S. Seott K. Stein Geschäftsfohrende Herausgeber

B. Eekmann J. K. Moser B.L. van der Waerden

B. Schoeneberg

Elliptic Modular Functions An Introduction

Translated [rom the German by J. R. Smart and E. A. Schwandt With 22 Figures

Springer-Verlag Berlin Heidelberg New York 1974

Bruno Schoeneberg Universität Hamburg

Geschäftsführende Herausgeber B. Eckmann Eidgenössische Technische Hochschule Zürich J. K. Moser Courant Institute of Mathematical Sciences, New York B. L. van der Waerden

Mathematisches Institut der Universität Zürich

AMS Subject Classifications (1970): Primary 30 A 58, 10 D 05 Secondary 20 H 10

ISBN-13: 978-3-642-65665-1 DOl: 10.1007/978-3-642-65663-7

This work is subject

LO

e-ISBN-13: 978-3-642-65663-7

copyright. AB fights are reser ....ed, \\lhethcr 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 mc ans, and storage:: in dala banks. Under ~ 54 of the German Copyright Law where co pies are made for other than pri\'atc use. a fee is payable Lo the puhlisher. the amount oflhe fee to be determined by agreement with the publlshcr. © by SpringerVerlag Berlin Hcidelberg 1974. Library of Congress Ca,.log Card Numbe. 73-8486. Softcover reprint ofthe hardcover 1st edition 1974

B. Schoeneberg

Elliptic Modular Functions An Introduction

Translated from the German by J.R. Smart and E.A. Schwandt With 22 Figures

Springer-Verlag New York Heidelberg Berlin 1974

Bruno Schoeneberg Universität Hamburg

Geschäftsführende Herausgeber B. Eckmann Eidgenössische Technische Hochschule Zürich J. K. Moser Courant Institute of Mathematical Sciences, New York B. L. van der Waerden

Mathematisches Institut der Universität Zürich

AMS Subject Classifications (1970): Primary 30 A 58, 10 D 05 Secondary 20 H 10

ISBN-13: 978-3-642-65665-1 DOl: 10.1007/978-3-642-65663-7

This work is subject

LO

e-ISBN-13: 978-3-642-65663-7

copyright. AB fights are reser ....ed, \\lhethcr 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 mc ans, and storage:: in dala banks. Under ~ 54 of the German Copyright Law where co pies are made for other than pri\'atc use. a fee is payable Lo the puhlisher. the amount oflhe fee to be determined by agreement with the publlshcr. © by SpringerVerlag Berlin Hcidelberg 1974. Library of Congress Ca,.log Card Numbe. 73-8486. Softcover reprint ofthe hardcover 1st edition 1974

Preface

This book is a fully detailed introduction to the theory of modular functions of a single variable. I hope that it will fill gaps which in view ofthe lively development ofthis theory have often been an obstacle to the students' progress. The study of the book requires an elementary knowled