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L Functions And The Oscillator Representation
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Book Synopsis L-Functions and the Oscillator Representation by : Stephen Rallis
Download or read book L-Functions and the Oscillator Representation written by Stephen Rallis and published by Springer. This book was released on 2006-11-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an L-function (associated to the standard representation of the L-group of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard L-functions, (ii) see-saw dual reductive pairs and (iii) Siegel-Weil formula. The book addresses readers who specialize in the theory of automorphic forms and L-functions and the representation theory of Lie groups. N
Book Synopsis Automorphic Representations, L-Functions and Applications: Progress and Prospects by : James W. Cogdell
Download or read book Automorphic Representations, L-Functions and Applications: Progress and Prospects written by James W. Cogdell and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27–30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin–Selberg L-functions (Bump, Ginzburg–Jiang–Rallis, Lapid–Rallis) the relative trace formula (Jacquet, Mao–Rallis) automorphic representations (Gan–Gurevich, Ginzburg–Rallis–Soudry) representation theory of p-adic groups (Baruch, Kudla–Rallis, Mœglin, Cogdell–Piatetski-Shapiro–Shahidi) p-adic methods (Harris–Li–Skinner, Vigneras), and arithmetic applications (Chinta–Friedberg–Hoffstein). The survey articles by Bump, on the Rankin–Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.
Book Synopsis Automorphic Forms, Representations and $L$-Functions by : A. Borel
Download or read book Automorphic Forms, Representations and $L$-Functions written by A. Borel and published by American Mathematical Soc.. This book was released on 1979 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains sections on Reductive groups, representations, Automorphic forms and representations.
Book Synopsis Relative Trace Formulas by : Werner Müller
Download or read book Relative Trace Formulas written by Werner Müller and published by Springer Nature. This book was released on 2021-05-18 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur’s trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.
Book Synopsis Eisenstein Series and Applications by : Wee Teck Gan
Download or read book Eisenstein Series and Applications written by Wee Teck Gan and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.
Book Synopsis Selected Works of Ilya Piatetski-Shapiro by : Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro
Download or read book Selected Works of Ilya Piatetski-Shapiro written by Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro and published by American Mathematical Soc.. This book was released on 2000 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt: This selection of papers of Ilya Piatetski-Shapiro represents almost 50 years of his mathematical activity. Included are many of his major papers in harmonic analysis, number theory, discrete groups, bounded homogeneous domains, algebraic geometry, automorphic forms, and automorphic L-functions. The papers in the volume are intended as a representative and accurate reflection of both the breadth and depth of Piatetski-Shapiro's work in mathematics. Some of his early works, such as those on the prime number theorem and on sets of uniqueness for trigonometric series, appear for the first time in English. Also included are several commentaries by his close colleagues. This volume offers an elegant representation of the contributions made by this renowned mathematician.
Book Synopsis Representation Theory, Number Theory, and Invariant Theory by : Jim Cogdell
Download or read book Representation Theory, Number Theory, and Invariant Theory written by Jim Cogdell and published by Birkhäuser. This book was released on 2017-10-19 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Representation Theory and Automorphic Forms by : T. N. Bailey
Download or read book Representation Theory and Automorphic Forms written by T. N. Bailey and published by American Mathematical Soc.. This book was released on 1997 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Modular Forms and Special Cycles on Shimura Curves. (AM-161) by : Stephen S. Kudla
Download or read book Modular Forms and Special Cycles on Shimura Curves. (AM-161) written by Stephen S. Kudla and published by Princeton University Press. This book was released on 2006-04-04 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "M" attached to a Shimura curve "M" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and Siegel modular forms of genus two respectively, valued in the Gillet-Soulé arithmetic Chow groups of "M". The two types of generating functions are related via an arithmetic inner product formula. In addition, an analogue of the classical Siegel-Weil formula identifies the generating function for zero-cycles as the central derivative of a Siegel Eisenstein series. As an application, an arithmetic analogue of the Shimura-Waldspurger correspondence is constructed, carrying holomorphic cusp forms of weight 3/2 to classes in the Mordell-Weil group of "M". In certain cases, the nonvanishing of this correspondence is related to the central derivative of the standard L-function for a modular form of weight 2. These results depend on a novel mixture of modular forms and arithmetic geometry and should provide a paradigm for further investigations. The proofs involve a wide range of techniques, including arithmetic intersection theory, the arithmetic adjunction formula, representation densities of quadratic forms, deformation theory of p-divisible groups, p-adic uniformization, the Weil representation, the local and global theta correspondence, and the doubling integral representation of L-functions.
Download or read book Motives written by and published by American Mathematical Soc.. This book was released on 1994-02-28 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Motives' were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, and to play the role of the missing rational cohomology. This work contains the texts of the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991.
Book Synopsis L-Functions and Arithmetic by : J. Coates
Download or read book L-Functions and Arithmetic written by J. Coates and published by Cambridge University Press. This book was released on 1991-02-22 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at presenting nontechnical explanations, all the essays in this collection of papers from the 1989 LMS Durham Symposium on L-functions are the contributions of renowned algebraic number theory specialists.
Book Synopsis Automorphic Representations of Unitary Groups in Three Variables by : Jonathan David Rogawski
Download or read book Automorphic Representations of Unitary Groups in Three Variables written by Jonathan David Rogawski and published by Princeton University Press. This book was released on 1990-09-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.
Download or read book Ring Theory written by Jose L. Bueso and published by Springer. This book was released on 2007-01-05 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this proceedings volume are selected research papers in different areas of ring theory, including graded rings, differential operator rings, K-theory of noetherian rings, torsion theory, regular rings, cohomology of algebras, local cohomology of noncommutative rings. The book will be important for mathematicians active in research in ring theory.
Book Synopsis Complex Analysis by : Steven G. Krantz
Download or read book Complex Analysis written by Steven G. Krantz and published by Springer. This book was released on 2006-11-14 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference gathered together a small group of people with similar interests in the geometric function theory of several complex variables. While the speeches were of a specialized nature, the papers in the proceedings are largely of a survey and speculative nature. The volume is intended to serve both students and researchers as an invitation to active new areas of research. The level of the writing has been intentionally set in such a way that the papers will be accessible to a broad audience.
Book Synopsis Global Analysis. Studies and Applications III by : Yurii G. Borisovich
Download or read book Global Analysis. Studies and Applications III written by Yurii G. Borisovich and published by Springer. This book was released on 2006-11-14 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Number-Theoretic Analysis by : Edmund Hlawka
Download or read book Number-Theoretic Analysis written by Edmund Hlawka and published by Springer. This book was released on 2006-11-14 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamical Systems by : James C. Alexander
Download or read book Dynamical Systems written by James C. Alexander and published by Springer. This book was released on 2006-11-14 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume reflect the richness and diversity of the subject of dynamics. Some are lectures given at the three conferences (Ergodic Theory and Topological Dynamics, Symbolic Dynamics and Coding Theory and Smooth Dynamics, Dynamics and Applied Dynamics) held in Maryland between October 1986 and March 1987; some are work which was in progress during the Special Year, and some are work which was done because of questions and problems raised at the conferences. In addition, a paper of John Milnor and William Thurston, versions of which had been available as notes but not yet published, is included.
