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Author : Ürtiş Çetin
Publisher : Unknown
Page : 144 pages
File Size : 41,6 Mb
Release : 2002
Category : Electronic
ISBN : MINN:31951P00801712J
Author : Anonim
Publisher : American Mathematical Soc.
Page : 694 pages
File Size : 54,5 Mb
Release : 1994-02-28
Category : Mathematics
ISBN : 9780821827987
'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.
Author : Uwe Jannsen,Jean-pierre Serre,Steven Kleiman
Publisher : American Mathematical Soc.
Page : 696 pages
File Size : 48,5 Mb
Release : 1994-02-28
Category : Mathematics
ISBN : 0821827995
Motives were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, to play the role of the missing rational cohomology, and to provide a blueprint for proving Weil's conjectures about the zeta function of a variety over a finite field. Over the last ten years or so, researchers in various areas--Hodge theory, algebraic $K$-theory, polylogarithms, automorphic forms, $L$-functions, $ell$-adic representations, trigonometric sums, and algebraic cycles--have discovered that an enlarged (and in part conjectural) theory of ``mixed'' motives indicates and explains phenomena appearing in each area. Thus the theory holds the potential of enriching and unifying these areas. These two volumes contain the revised texts of nearly all the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991. A number of related works are also included, making for a total of forty-seven papers, from general introductions to specialized surveys to research papers.
Author : Chen Wan
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 54,6 Mb
Release : 2019-12-02
Category : Education
ISBN : 9781470436865
Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author proves a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, the author proves the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.
Author : James W. Cogdell,Dihua Jiang,Stephen S. Kudla,David Soudry,Robert J. Stanton
Publisher : Walter de Gruyter
Page : 441 pages
File Size : 40,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110892703
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.
Author : Stephen Rallis
Publisher : Springer
Page : 254 pages
File Size : 54,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540477617
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
Author : Leon Ehrenpreis
Publisher : American Mathematical Soc.
Page : 378 pages
File Size : 48,6 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821814840
Author : Anonim
Publisher : Unknown
Page : 304 pages
File Size : 54,9 Mb
Release : 1990
Category : Mathematics
ISBN : CORNELL:31924084303704
Author : James W. Cogdell,Freydoon Shahidi,David Soudry
Publisher : American Mathematical Soc.
Page : 454 pages
File Size : 47,5 Mb
Release : 2014-04-01
Category : Mathematics
ISBN : 9780821893944
This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.
Author : Henri Darmon,Shou-wu Zhang
Publisher : Cambridge University Press
Page : 386 pages
File Size : 49,6 Mb
Release : 2004-06-21
Category : Mathematics
ISBN : 052183659X
Thirteen articles by leading contributors on the history of the Gross-Zagier formula and its developments.
Author : Haruzo Hida,Dinakar Ramakrishnan,Freydoon Shahidi
Publisher : JHU Press
Page : 946 pages
File Size : 49,7 Mb
Release : 2004-03-11
Category : Mathematics
ISBN : 0801878608
In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic forms, principally via the associated L-functions, representation theory, and geometry. Because these themes are at the cutting edge of a central area of modern mathematics, and are related to the philosophical base of Wiles' proof of Fermat's last theorem, this book will be of interest to working mathematicians and students alike. Never previously published, the contributions to this volume expose the reader to a host of difficult and thought-provoking problems. Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth. New and powerful results are being proved, radically and continually changing the field's make up. Contributions to Automorphic Forms, Geometry, and Number Theory will likely lead to vital interaction among researchers and also help prepare students and other young mathematicians to enter this exciting area of pure 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.
Author : Atsushi Ichino,Kartik Prasanna
Publisher : American Mathematical Society
Page : 214 pages
File Size : 46,7 Mb
Release : 2021-02-23
Category : Mathematics
ISBN : 9781470448943
This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura's algebraicity conjectures on these periods. It also provides a strategy to attack this conjecture by reformulating it in terms of integrality properties of the theta correspondence for quaternionic unitary groups. The methods and constructions of the book are expected to have applications to other problems related to periods, such as the Bloch-Beilinson conjecture about special values of $L$-functions and constructing geometric realizations of Langlands functoriality for automorphic forms on quaternion algebras.
Author : Wee Teck Gan,Stephen S. Kudla,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 53,5 Mb
Release : 2007-12-22
Category : Mathematics
ISBN : 9780817646394
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.
Author : Anonim
Publisher : Unknown
Page : 1084 pages
File Size : 45,7 Mb
Release : 2005
Category : Mathematics
ISBN : UOM:39015062317220
Author : Sinnou David
Publisher : Cambridge University Press
Page : 227 pages
File Size : 51,7 Mb
Release : 1996-11-07
Category : Mathematics
ISBN : 9780521585491
This book covers the whole spectrum of number theory, and is composed of contributions from some of the best specialists worldwide.