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. Download Citation on ResearchGate | Automorphic forms on Adele groups / by Stephen S. Gelbart | “Expanded from notes mimeographed at Cornell in May of.

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I understand that Hecke characters relate to adeles, but you seem to be implying that Hecke characters lifting to characters on adeles in the first example of a classical modular form becoming a flrms on adeles. Quotients of this group appear as Galois groups of extensions of spaces of modular forms, so they might be given representations by acting on these spaces? For the cuspidal spectrum see [Don82] of the references, too.

fkrms Other books in this series. To answer the question in your second comment I’ll say this: Sign up or log in Sign up using Google. Again you can define a Hecke algebra. Home Questions Tags Users Unanswered.

Automorphic Forms on Adele Groups. (AM-83), Volume 83

AMVolume Vladimir Voevodsky. Automorphic Forms on a Quaternion Algebra show more.

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. Post as a guest Name. A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula.

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Dispatched from the UK in 4 business days When will my order arrive? As you probably know, the real and imaginary parts of a holomorphic function are harmonic, i. At least part of this started with Langlands classification fofms the admissible representation of real reductive groups.

How is representation theory used in modular/automorphic forms? – MathOverflow

Dynamics in One Complex Variable. One of my ideas might be fruitful, or they all might uatomorphic nothing to do with why representation theory connects to modular functions. Wait, how does a Hecke character give a modular form?

Automorphic Forms on Adele Groups.

Sign up using Email and Password. And if you want to get into the whole automorphic representations on adeles groups then some knowledge of algebraic groups and representations of reductive algebraic groups.

Sign up using Facebook. I’m asking this in part because I imagine a number of students with similar background as I have would have learned about modular forms and thus might be interested to understand how they relate to representation theory, despite not having an extensive background in more advanced results in algebraic geometry and commutative algebra needed for advanced study in the field.

These correspondences should be nice in that things that happen on one side should correspond to things happening on the other.

The point is that I’m looking for basic ideas that someone with an elementary background might be able to understand.

I also added “reference request” because I imagine there might be a text which is at my level and discusses these ideas. To get into the Langlands program there’s the book an introduction to the Langlands program google books you could look at. AMVolume 82 Joan S.

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Automorphic Forms on Adele Groups. (AM), Volume 83 : Stephen S. Gelbart :

There is certainly an abundance of advanced books on Galois representations and automorphic forms. AM-7Volume 7 Paul R. The Trace Formula for GL 2 A one line answer: You should not see modular forms or Hecke characters as functions on these spaces.

The Classical Theory 2. Actually, that book does seem particularly good as an answer to this question. Or is it just that I need to learn some yroups algebraic geometry? It is a pity that things gelbaft these don’t occur in complex analysis courses.

Cycles, Transfers, and Motivic Homology Theories. The link is as follows: From this view point, the algebraic geometry side of the picture oh simply as the source for proving instances of the Langlands conjectures. Here are two fairly old books that explain and exploit representation theory behind the theory of theta functions and automorphic forms neither assuming adwle using algebraic geometry and commutative algebra in a serious way:.

It’s impossible to determine ahead of time whether you know enough to fully understand these books certainly, functional analysis would be helpful to knowbut the good news is that you can start right away and pick up some pieces as you go.