Preface I was captivated by a group of enthusiastic Spanish mathematicians whose desire for cultivating modern number theory I enjoyed recently during two memorable events, the first at the summer school in Santander, 1992, and the second while visiting the Universidad Aut´ onoma in Madrid in June 1993. These notes are an expanded version of a series of eleven lectures I delivered in Madrid1. They are more than a survey of favorite topics, since proofs are given for all important results. However, there is a lot of basic material which should have been included for completeness, but was not because of time and space limitations. Instead, to make a comprehensive exposition we focus on issues closely related to the the spectral aspects of automorphic forms (as opposed to the arithmetical aspects, to which I intend to return on another occasion). Primarily, the lectures are addressed to advanced graduate students. I hope the student will get inspiration for his own adventures in the field. This is a goal which Professor Antonio ordoba has a vision of pursuing throughout the new volumes to be published by the Revista Matem´atica Iberoamericana. I am pleased to contribute to part of his plan. Many people helped me prepare these notes for publication. In particular I am grateful to Fernando Chamizo, Jos´ e Luis Fern´ andez, Charles Mozzochi, Antonio anchez-Calle and Nigel Pitt for reading and correcting an early draft. I also acknowledge the substantial work in the technical preparation of this text by Domingo Pestana and Mar´ ıa Victoria Meli´ an, without which this book would not exist. New Brunswick, October 1994 Henryk Iwaniec 1 I would like to thank the participants and the Mathematics Department for their warm hospitality and support. ix
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