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Maass Forms and the Spectral Problem 2. Basic Lie Theory 3. Discreteness of the Spectrum 4. Basic Representation Theory 6.

Unitaricity and Intertwining Integrals 7. Representations and the Spectral Problem 8. Whittaker Models 9. Automorphic Forms and Representations 3. Automorphic Representations of GL n 4. The Tensor Product Theorem 5.

Whittaker Models and Automorphic Forms 6. Adelization of Automorphic Forms 7. Eisenstein Series and Intertwining Integrals 8. The Rankin-Selberg Method 9. The Global Langlands Conjectures GL 2 over a Finite Field 2. Smooth and Admissible Representations 3. Distributions and Sheaves 4. Whittaker Models and the Jacquet Functor 5.

The Principal Series Representations 6. Spherical Representations 8. Supercuspidals and the Weil Representation 9. I felt that there was a need for a book which would present the subject in a style which was accessible, yet based on complete proofs, revealing clearly the uniqueness principles which underlie the basic constructions. Since I have been lecturing on automorphic forms and representation theory at Stanford and the MSRI , and this book is the end result.

The level of this book is intermediate between an advanced textbook and a monograph. I hope that it will be found interesting by experts as well as graduate students. Its aim is to cover a substantial portion of the theory of automorphic forms on GL 2.

There are significant omissions from our treatment, most seriously the Selberg Trace Formula. It has not been my aim to achieve complete coverage of the topics treated, or to write a reference book. I feel that the existing reference material is adequate, and it was not feasible to cover any single topic with the thoroughness I would have liked.

Rather, it was my aim to treat my subject matter with some degree of depth. I hope that the reader will begin studying the reference material such as the Corvallis volume and above all Jacquet and Langlands in the course of reading this book.

If I have done my job well, the task of approaching Jacquet and Langlands should be made easier by the current volume. Thanks also to Lauren Cowles of Cambridge University Press for her interest in the manuscript and for her guidance, to Ellen Tirpak and the staff at TechBooks for their expert handling of the manuscript, to Reid Augustin for helping me set up my Linux machine, and to the MSRI for their help and support during And thank you, my wife Kathi, and my parents Kenneth and Ellen Bump, for your support, which was always there when I needed it most.


Automorphic Forms and Representations

Phone numbers and estimated transportation charges are also listed. Automorphic Forms and Representations. Automorphic Forms, Representations, and Combinatorics: Read, highlight, and take notes, across web, tablet, and phone. Persi Diaconis Stanford University. Daniel Bump has been a leading mathematician in automorphic forms, representation theory and number theory for over three decades. Situated in downtown Palo Alto, the Cardinal is within walking distance of shopping and many fine dining establishments.


Daniel Bump

Maass Forms and the Spectral Problem 2. Basic Lie Theory 3. Discreteness of the Spectrum 4. Basic Representation Theory 6. Unitaricity and Intertwining Integrals 7.

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