Selberg Zeta Functions and Transfer Operators An Experimental Approa
This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the d
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Markus Szymon Fraczek
Selberg Zeta Functions and Transfer Operators An Experimental Approach to Singular Perturbations
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
2139
More information about this series at http://www.springer.com/series/304
Markus Szymon Fraczek
Selberg Zeta Functions and Transfer Operators An Experimental Approach to Singular Perturbations
123
Markus Szymon Fraczek Mathematics Institute University of Warwick Coventry, United Kingdom
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-51294-5 DOI 10.1007/978-3-319-51296-9
ISSN 1617-9692 (electronic) ISBN 978-3-319-51296-9 (eBook)
Library of Congress Control Number: 2017933469 Mathematics Subject Classification (2010): 11M36, 37C30, 34L16, 35B25, 11M35, 33F05, 58J50, 58J37, 58J51 © Springer International Publishing AG 2017 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
1
2
Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.1 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.2 Groups and Geometry.. . . . . . . . . . . . . . . . .
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