By Hida H., et al. (eds.)
In Contributions to Automorphic types, Geometry, and quantity idea, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi assemble a distinct staff of specialists to discover automorphic types, largely through the linked L-functions, illustration concept, and geometry. simply because those issues are on the leading edge of a important zone of recent arithmetic, and are relating to the philosophical base of Wiles' facts of Fermat's final theorem, this e-book can be of curiosity to operating mathematicians and scholars alike. by no means formerly released, the contributions to this quantity reveal the reader to a number of inauspicious and thought-provoking problems.Each of the extreme and memorable mathematicians during this quantity makes a distinct contribution to a box that's at the moment seeing explosive development. New and strong effects are being proved, substantially and consistently altering the field's make up. Contributions to Automorphic types, Geometry, and quantity idea will most probably result in very important interplay between researchers and in addition aid organize scholars and different younger mathematicians to go into this fascinating zone of natural mathematics.Contributors: Jeffrey Adams, Jeffrey D. Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Hervé Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vignéras, Jean-Loup Waldspurger.
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Additional info for Contributions to automorphic forms, geometry, and number theory: in honor of Joseph Shalika
Knapp and P. Trapa from the 1998 Park City Conference . The proceedings of the 1996 Edinburgh Conference  include a number of expository articles, including one on the Langlands program by A. Knapp . We make repeated use of the Langlands classification (sometimes referred to as the Langlands–Knapp–Zuckerman classification) and its equivalent form, the Vogan classification. A summary of the statements, with references to more details, may be found in Sections 3 and 4 of D. Vogan’s “The unitary dual of G 2 ” .
Shalika SD with the product defined by (ii) is a complex algebra. It is known that SD is dense in the commuting algebra of the induced representation D. Now let D be one of the following irreducible unitary representations of K : D( , ρ, V ) for ρ 2 = 1, D + ( , V ), or D − ( , V ) when V / is unramified, and D( , ρ0 , V ) when V / is ramified. 1. The algebras SD have complex dimension one. ) Proof. Let F belong to SD . Since (say, by elementary divisors) G= KτmK, where m≥0 τ = 0 , π −1 π 0 F is determined by its value on τ m for m ≥ 0.
In this section I will obtain irreducible representations of K = SL(2, Op) by restricting the representations of G = SL(2, ) to that subgroup. Some of these representations appear in a series of papers of Kloosterman . K -stable subspaces of D( , V ). For the moment, I return to the case when V is an even-dimensional metric vector space over . For a lattice in V and a of , let H , denote the Hilbert subspace of hV consisting of those sublattice complex-valued functions h on V satisfying (i) the support of h is contained in (ii) h(x + λ ) = h(x) for all λ ∈ , .