Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory
This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of mo
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Johannes Blümlein Carsten Schneider Peter Paule Editors
Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory
Texts & Monographs in Symbolic Computation A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria
Founded by Bruno Buchberger, Research Institute for Symbolic Computation, Hagenberg, Austria Series editor Peter Paule, Hagenberg, Austria
Mathematics is a key technology in modern society. Symbolic Computation is on its way to become a key technology in mathematics. “Texts and Monographs in Symbolic Computation” provides a platform devoted to reflect this evolution. In addition to reporting on developments in the field, the focus of the series also includes applications of computer algebra and symbolic methods in other subfields of mathematics and computer science, and, in particular, in the natural sciences. To provide a flexible frame, the series is open to texts of various kind, ranging from research compendia to textbooks for courses.
More information about this series at http://www.springer.com/series/3073
Johannes Blümlein Carsten Schneider Peter Paule •
Editors
Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory
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Editors Johannes Blümlein Deutsches Elektronen-Synchrotron, DESY Zeuthen, Germany Carsten Schneider Research Institute for Symbolic Computation (RISC) Johannes Kepler University Linz Linz, Austria
Peter Paule Research Institute for Symbolic Computation (RISC) Johannes Kepler University Linz Linz, Austria
ISSN 0943-853X ISSN 2197-8409 (electronic) Texts & Monographs in Symbolic Computation ISBN 978-3-030-04479-4 ISBN 978-3-030-04480-0 (eBook) https://doi.org/10.1007/978-3-030-04480-0 Library of Congress Control Number: 2018961736 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Spri
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