Last edited by Fedal
Wednesday, August 5, 2020 | History

7 edition of Automorphic forms on Adele groups found in the catalog.

# Automorphic forms on Adele groups

## by Stephen S. Gelbart

Written in English

Subjects:
• Representations of groups,
• Automorphic forms,
• Linear algebraic groups,

• Edition Notes

Classifications The Physical Object Statement by Stephen S. Gelbart. Series Annals of mathematics studies ;, no. 83 LC Classifications QA171 .G39 1975 Pagination x, 267 p. ; Number of Pages 267 Open Library OL5059590M ISBN 10 0691081565 LC Control Number 74023388

We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and de ne all objects over the (rational) adeles A, thereby also paving the way for connections to number theory, representation theoryFile Size: 3MB.   Automorphic representations: a short list of books posted by Jason Polak on Saturday July 6, with 1 comment and filed under number-theory, representation-theory | Tags: automorphic representations. This is a short list of books to get you started on learning automorphic representations.

Princeton University Press is proud to have published the Annals of Mathematics Studies since One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the 20th century. Automorphic Forms on Adele Groups. This book provides the first coherent.   The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Author: George Lusztig.

Deformations of p-divisible groups 45 Serre-Tate theory 47 Deformation theory of points of Sh 47 Chapter 8. Topological automorphic forms 51 The generalized Hopkins-Miller theorem 51 The descent spectral sequence 54 Application to Shimura stacks 56 Chapter 9. Relationship to automorphic forms 57 Alternate. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic.

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Automorphic Forms on Adele Groups. (AM) Book Description: Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6.

Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. The Classical Theory 2. Automorphic Forms and the Decomposition of L2 (PSL (2,R) 3. Automorphic Forms as Functions on the Adele Group of GL (2) 4. The Representations of GL (2) over Local and Global Fields 5.

Cusp Forms and Representations of the Adele Group of GL (2) 6. Hecke Theory for GL (2) 7. The Construction of a Special Class of. This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups.

Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The classical theory --Automorphic forms and the decomposition of L² --Automorphic forms as functions on the adele group of GL(2) --The representations of GL(2) over local and global fields --Cusp forms and representations of the adele group of GL(2) --The construction of a special class of automorphic forms --Eisenstein series and the.

Automorphic Forms on Adele Groups. (AM) (Annals of Mathematics Studies) (Annals of Mathematics Studies (83)) First Edition by Stephen S. Gelbart (Author) › Visit Amazon's Stephen S. Gelbart Page. Find all the books, read about the author, and more. Cited by: automorphic forms as functions on the adele group of gl(2), pg.

40* 4. THE REPRESENTATIONS OF GL(2) OVER LOCAL AND GLOBAL FIELDS, pg. 54* 5. CUSP FORMS AND REPRESENTATIONS OF THE ADELE GROUP OF GL(2), pg. 79* 6. The book features extensive foundational material on the representation theory of GL(1) and GL(2) over local fields, the theory of automorphic representations, L-functions and advanced topics such as the Langlands conjectures, the Weil representation, the Rankin–Selberg method and the triple L-function, examining this subject matter from many Cited by: Automorphic Forms and Representations (Cambridge Studies in Advanced Mathematics Book 55) - Kindle edition by Bump, Daniel.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Automorphic Forms and Representations (Cambridge Studies in Advanced Mathematics Book 55)/5(7).

There are the lecture notes "AN INTRODUCTION TO AUTOMORPHIC REPRESENTATIONS" by Jayce R. Getz, which start on the background on adele rings, then treat algebraic groups and automorphic representations, Nonarchimedian Hecke algebras, a bit of archimedian representation theory, before in chapter $6$ it comes to automorphic forms on adele groups.

This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and Price: $Find many great new & used options and get the best deals for Annals of Mathematics Studies: Automorphic Forms and Adele Groups 83 by Stephen S. Gelbart (, Paperback) at the best online prices at eBay. Free shipping for many products. Automorphic Forms on Adele Groups. (AM), Volume As for suggestions on what to read, I found Gelbart’s book Automorphic forms on adele groups pretty readable. Is there rorms connection here. The most comprehensive reference is the Corvallis proceedings available freely at ams. Automorphic Forms and Automorphic Representations Wee Teck Gan References: A. Borel, Automorphic forms on SL2(R) - D. Bump, Automorphic forms and repre-sentations - S. Gelbart, Automorphic forms on adele groups 1. Introduction About ninety years ago, Ramanujan considered the following power series of q. Modern analysis of automorphic forms by examples Paul Garrett version Aug c Paul Garrett This is a prepublication version of a book to be published by Cambridge University Press, Per contractual agreement, I can keep a PDF copy on-line (especially for corrections and updates), and. Gelbart, Stephen S. Automorphic Forms on Adele Groups. (AM), Volume Series:Annals of Mathematics Studies PRINCETON UNIVERSITY PRESS. Automorphic Representations of Adele Groups. We have defined the space A(G, Γ) of auto- morphic forms with respect to an arithmetic group Γ of G (a reductive. As for suggestions on what to read, I found Gelbart's book Automorphic forms on adele groups pretty readable. This will get you through some of what I've written in the first two paragraphs for the group$\mathrm{GL}(2)$. The most comprehensive reference is the Corvallis proceedings available freely at. I was going through the book Automorphic forms on Adele groups by Stephen S. Gelbert and in the second page of first chapter I got a statement like all Fuchsian groups have a finite numbers of Γ-Stack Exchange Network. Stack Exchange network consists of Q&A communities including Stack Overflow, the. The subject matter of these Notes is the interplay between the theory of automorphic forms and group representations. One goal is to interpret some recent developments in this area, most significantly the theory of Jacquet-Langlands, working out, whenever possible, explicit consequences and connections with the classical : Stephen S. Gelbart. Buy Automorphic Forms and Representations (Cambridge Studies in Advanced Mathematics) by Daniel Bump (ISBN: ) from Amazon's Book Store. Everyday low /5(5).$\begingroup$@user Well, at the moment only the most basic case of the additive divisor problem has been treated with automorphic forms, i.e. the problem of summing$\tau(n)\tau(n+h)$or$\tau(n)\tau(h-n)\$, but for this case we have rather strong results.

I recommend Yoichi Motohashi's article (Annales scientifiques de l'Ecole Normale Suprieure, ) and book (Cambridge University. In mathematics, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and ed by Robert Langlands (, ), it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and seen as the single biggest project in modern.Introduction.

A cusp form is distinguished in the case of modular forms for the modular group by the vanishing of the constant coefficient a 0 in the Fourier series expansion (see q-expansion) ∑. This Fourier expansion exists as a consequence of the presence in the modular group's action on the upper half-plane via the transformation ↦ + For other groups, there may be some translation.Gelbart, Stephen S.

Automorphic forms on adele groups. No. Princeton University Press, ; Getz, J. R.,Hahn H. An Introduction to Automorphic Representations with a view toward Trace Formulae /; Goldfeld, Dorian.

Automorphic forms and L-functions for the group GL (n, R). Vol. Cambridge University Press,