Zeta Integrals Schwartz Spaces And Local Functional Equations

Author : Wen-Wei Li
Publisher : Springer
ISBN 13 : 3030012883
Total Pages : 148 pages
Book Rating : 4.85/5 ( download)

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Download or read book Zeta Integrals, Schwartz Spaces and Local Functional Equations written by Wen-Wei Li and published by Springer. This book was released on 2018-11-02 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.

Author : Volker Heiermann
Publisher : Springer
ISBN 13 : 3319952315
Total Pages : 364 pages
Book Rating : 4.14/5 ( download)

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Download or read book Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms written by Volker Heiermann and published by Springer. This book was released on 2018-10-01 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a panorama of the diverse activities organized by V. Heiermann and D. Prasad in Marseille at the CIRM for the Chaire Morlet event during the first semester of 2016. It assembles together expository articles on topics which previously could only be found in research papers. Starting with a very detailed article by P. Baumann and S. Riche on the geometric Satake correspondence, the book continues with three introductory articles on distinguished representations due to P. Broussous, F. Murnaghan, and O. Offen; an expository article of I. Badulescu on the Jacquet–Langlands correspondence; a paper of J. Arthur on functoriality and the trace formula in the context of "Beyond Endoscopy", taken from the Simons Proceedings; an article of W-W. Li attempting to generalize Godement–Jacquet theory; and a research paper of C. Moeglin and D. Renard, applying the trace formula to the local Langlands classification for classical groups. The book should be of interest to students as well as professional researchers working in the broad area of number theory and representation theory.

Author : Werner Müller
Publisher : Springer
ISBN 13 : 3319948334
Total Pages : 453 pages
Book Rating : 4.31/5 ( download)

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Download or read book Geometric Aspects of the Trace Formula written by Werner Müller and published by Springer. This book was released on 2018-10-11 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups. Based on research presented at the 2016 Simons Symposium on Geometric Aspects of the Trace Formula that took place in Schloss Elmau, Germany, the volume contains both original research articles and articles that synthesize current knowledge and future directions in the field. The articles discuss topics such as the classification problem of representations of reductive groups, the structure of Langlands and Arthur packets, interactions with geometric representation theory, and conjectures on the global automorphic spectrum. Suitable for both graduate students and researchers, this volume presents the latest research in the field. Readers of the first volume Families of Automorphic Forms and the Trace Formula will find this a natural continuation of the study of the trace formula.

Author : Dihua Jiang
Publisher : American Mathematical Society
ISBN 13 : 1470469073
Total Pages : 104 pages
Book Rating : 4.78/5 ( download)

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Download or read book Harmonic Analysis and Gamma Functions on Symplectic Groups written by Dihua Jiang and published by American Mathematical Society. This book was released on 2024-04-17 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Author : Dorian Goldfeld
Publisher : Cambridge University Press
ISBN 13 : 1139500139
Total Pages : 571 pages
Book Rating : 4.35/5 ( download)

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Download or read book Automorphic Representations and L-Functions for the General Linear Group: Volume 1 written by Dorian Goldfeld and published by Cambridge University Press. This book was released on 2011-04-21 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.

Author : Nicole Bopp
Publisher : American Mathematical Soc.
ISBN 13 : 0821836234
Total Pages : 250 pages
Book Rating : 4.31/5 ( download)

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Download or read book Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces written by Nicole Bopp and published by American Mathematical Soc.. This book was released on 2005 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intends to prove a functional equation for a local zeta function attached to the minimal spherical series for a class of real reductive symmetric spaces.

Author : Marcus du Sautoy
Publisher : Springer Science & Business Media
ISBN 13 : 354074701X
Total Pages : 217 pages
Book Rating : 4.17/5 ( download)

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Download or read book Zeta Functions of Groups and Rings written by Marcus du Sautoy and published by Springer Science & Business Media. This book was released on 2008 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.

Author : Miki Hirano
Publisher : American Mathematical Society
ISBN 13 : 1470452774
Total Pages : 136 pages
Book Rating : 4.73/5 ( download)

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Download or read book Archimedean Zeta Integrals for $GL(3)times GL(2)$ written by Miki Hirano and published by American Mathematical Society. This book was released on 2022-07-18 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Author : Zhi Qi
Publisher : American Mathematical Society
ISBN 13 : 1470443252
Total Pages : 123 pages
Book Rating : 4.52/5 ( download)

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Download or read book Theory of Fundamental Bessel Functions of High Rank written by Zhi Qi and published by American Mathematical Society. This book was released on 2021-02-10 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.

Author : Jun-ichi Igusa
Publisher : American Mathematical Soc.
ISBN 13 : 0821829076
Total Pages : 246 pages
Book Rating : 4.73/5 ( download)

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Download or read book An Introduction to the Theory of Local Zeta Functions written by Jun-ichi Igusa and published by American Mathematical Soc.. This book was released on 2000 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory presentation to the theory of local zeta functions. Viewed as distributions, and mostly in the archimedean case, local zeta functions are also called complex powers. The volume contains major results on analytic and algebraic properties of complex powers by Atiyah, Bernstein, I. M. Gelfand, S. I. Gelfand, and Sato. Chapters devoted to $p$-adic local zeta functions present Serre's structure theorem, a rationality theorem, and many examples found by the author. The presentation concludes with theorems by Denef and Meuser. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.