Modular Forms of Level One
We will use the topology on the extended upper half-plane ℍ* to define what it means for f(z) to be holomorphic at the cusp i∞.
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M. Ram Murty Michael Dewar Hester Graves
Problems in the Theory of Modular Forms
HBA Lecture Notes in Mathematics IMSc Lecture Notes in Mathematics
Series Editor Sanoli Gun, Institute of Mathematical Sciences, Chennai, Tamil Nadu, India Editorial Board R. Balasubramanian, Institute of Mathematical Sciences, Chennai Abhay G. Bhatt, Indian Statistical Institute, New Delhi Yuri F. Bilu, Université Bordeaux I, France Partha Sarathi Chakraborty, Institute of Mathematical Sciences, Chennai Carlo Gasbarri, University of Strasbourg, Germany Anirban Mukhopadhyay, Institute of Mathematical Sciences, Chennai V. Kumar Murty, University of Toronto, Toronto D.S. Nagaraj, Institute of Mathematical Sciences, Chennai Olivier Ramaré, Centre National de la Recherche Scientifique, France Purusottam Rath, Chennai Mathematical Institute, Chennai Parameswaran Sankaran, Institute of Mathematical Sciences, Chennai Kannan Soundararajan, Stanford University, Stanford V.S. Sunder, Institute of Mathematical Sciences, Chennai
About the Series The IMSc Lecture Notes in Mathematics series is a subseries of the HBA Lecture Notes in Mathematics series. This subseries publishes high-quality lecture notes of the Institute of Mathematical Sciences, Chennai, India. Undergraduate and graduate students of mathematics, research scholars, and teachers would find this book series useful. The volumes are carefully written as teaching aids and highlight characteristic features of the theory. The books in this series are co-published with Hindustan Book Agency, New Delhi, India.
More information about this series at http://www.springer.com/series/15465
M. Ram Murty Michael Dewar Hester Graves •
Problems in the Theory of Modular Forms
123
M. Ram Murty Department of Mathematics and Statistics Queen’s University Kingston, ON, Canada
Hester Graves University of Michigan Ann Arbor, MI, USA
Michael Dewar Queen’s University Kingston, ON, Canada
This work is a co-publication with Hindustan Book Agency, New Delhi, licensed for sale in all countries in electronic form only. Sold and distributed in print across the world by Hindustan Book Agency, P-19 Green Park Extension, New Delhi 110016, India. ISBN: 978-93-80250-72-4 © Hindustan Book Agency 2016. ISSN 2509-8071 (electronic) HBA Lecture Notes in Mathematics ISSN 2509-8098 (electronic) IMSc Lecture Notes in Mathematics ISBN 978-981-10-2651-5 (eBook) DOI 10.1007/978-981-10-2651-5 Library of Congress Control Number: 2016952892 © Springer Science+Business Media Singapore 2016 and Hindustan Book Agency 2016 This work is subject to copyright. All rights in this online edition are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of reuse of illustrations, recitation, broadcasting, 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
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