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This book contains selected papers based on talks given at the "Representation Theory, Number Theory, and Invariant Theory" conference held at Yale University from June 1 to June 5, 2015. The meeting and this resulting volume are in honor of Professor Roger Howe, on the occasion of his 70th birthday, whose work and insights have been deeply influential in the development of these fields. The speakers who contributed to this work include Roger Howe´s doctoral students, Roger Howe himself, and other world renowned mathematicians. Topics covered include automorphic forms, invariant theory, representation theory of reductive groups over local fields, and related subjects.

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Euler-Poincaré Characteristic for the Oscillator Representation (Adams, Prasad, Savin).- Problems Beyond Endoscopy (Arthur).- Unipotent Representations and the Dual Pair Correspondence (Barbasch).- On the Elliptic Nonabelian Fourier Transform for Unipotent Representations of p -adic Groups (Ciubotaru, Opdam).- Derivatives and L-functions for GL n (Cogdell, Piatetski-Shapiro).- The Howe Duality Conjecture: Quaternionic Case (Gan, Sun).- Estimates on Eisenstein Distributions for Reciprocals of p -adic L -functions: The Case of Irregular Primes (Gelbart, Greenberg, Miller, Shahidi).- Small Representations of Finite Classical Groups (Gurevitch, Howe).- Period Relations and Special Values of Rankin-Selberg L -functions (Harris, Lin).- Standard Monomial Theory for Harmonics in Classical Invariant Theory (Howe, Kim, Lee).- Automorphic Integral Transforms for Classical Groups II: Twisted Descents (Jiang, Zhang).- Construction of Tame Types (Kim, Yu).- Global Analysis by Hidden Symmetry (Kobayashi).- Le Lemme Fondamental Pour L´endoscopie Tordue: le CAS Oë le Groupe Endoscopique Elliptique Non Ramifié Est un Tore (Lemaire, Waldspurger).- Paquets d´Arthur Spéciaux Unipotents aux Places Archimédiennes et Correspondence de Howe (Moeglin).- Computations with Bernstein Projectors of SL (2) (Moy).- Some New Supercuspidal Representations (Reeder).- Plancherel Decomposition of Howe Duality and Euler Factorization of Automorphic Functionals (Sakellaridis).- On the Conservation Conjectures of Kudla and Rallis (Sun, Zhu).- An Analogue of the Kostant-Rallis Multiplicity Theorem for th -Group Harmonics (Wallach).

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