AUTOMORPHIC FORMS AND REPRESENTATIONS BUMP PDF

The Casimir operator condition says that some Laplacians [ citation needed ] have F as eigenfunction; this ensures that F has excellent analytic properties, but whether it is actually a complex-analytic function depends on the particular case. The values of j may be complex numbers, or in fact complex square matrices, corresponding to the possibility of vector-valued automorphic forms. The cocycle condition imposed on the factor of automorphy is something that can be routinely checked, when j is derived from a Jacobian matrix , by means of the chain rule. History[ edit ] Before this very general setting was proposed around , there had already been substantial developments of automorphic forms other than modular forms. The Hilbert modular forms also called Hilbert-Blumenthal forms were proposed not long after that, though a full theory was long in coming.

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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.

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Daniel Bump

Daniel Bump has been a leading mathematician in automorphic forms, representation theory and number theory for over three decades. Registration Use the following link to register: Account Options Sign in. See schedule for details. Conference participants can register and pick up information packets, name badges, etc. David Kazhdan Hebrew Univ. Dorian Goldfeld Columbia Univ.

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Automorphic Forms and Representations

Eventually, full-sized posters in PDF format will be linked below. This has been changed to Day 1 Announcements Conference participants can register and pick up information packets, name badges, etc. Light breakfast and coffee will be available. See schedule for details.

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