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

This gives an inkling of the connection. I suggest you take a look at Borel’s article Introduction to automorphic forms in the Boulder conference available freely at ams. The Best Books of You might also be interested in chapter 7 of An Introduction to the Langlands Program: What I’m wondering is more simple: These correspondences should be automorpphic in that things that happen on one side should correspond to things happening on the other.

Thus automorphhic books on automorphic forms e. There are numerous variations of this: In fact, while recently the role of Galois representations has been highlighted Langlands program, fofms theoremthis is an entirely separate and higher level issue compared with the basic dictionary between modular forms and automorphic representations.

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

The link is as follows: Email Required, but never shown. The point is that I’m looking for basic ideas that someone with an elementary background might be able to understand.

Well the basic link to representation theory is that modular forms and automorphic forms can be viewed as functions in representation spaces of reductive groups. Home Contact Us Help Free delivery worldwide. Is there a connection here? Probably the most notable example is monstrous moonshine. Other books in this series. But hopefully what I’ve written has helped you out a bit.


See Bump’s book section 2. Check out the top books of the year on our page Best Books of The right regular representation on an locally compact abelian groups is in direct connection with its Fourier transform.

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Here, too, the results from representation theory can be translated back into information about theta functions. Markov Processes from K. A one line answer: Dynamics in One Complex Variable. Academic Press, original edition published in Russian in Looking for beautiful books? This gives a representation.

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But yes, to get a good understanding of the basics Lie theory is required e. AMVolume 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 theory.

Radically Elementary Probability Theory. Pretty much the only way to take an automorphic representation and prove that it has an associated Galois representation is to construct a geometric object whose cohomology has both an action of the Hecke algebra and the Galois group and decompose it into pieces and pick out the one you want. What is the basic connection between modular forms and representation theory? For details, I’d refer you to any one of the books I suggested. Sign up or log in Sign up using Google.

Such as, giving a source or writing a small exposition? Is it Lie theory and if so what aspects of it? Since you mentioned Galois representations, I can briefly discuss the simplest version of the connection there and point you to Diamond and Shurman’s excellent book which discusses modular forms with an aim towards this perspective. Introduction to Algebraic K-Theory. Description This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups.


The point of listing ideas is to show the kind of intuition I might be looking for. The underlying theme is the decomposition of the regular representation of the adele group of GL 2.

I have a basic grounding in the complex analytic theory of modular forms their dimension formulas, how they classify isomorphism classes of elliptic curves, some basic examples of level N modular forms and their relation to torsion points on elliptic curves, series expansions, theta functions, Hecke operators.

Since the action is associative, i. Wait, how does a Hecke character give a modular form? By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. One remark how I think about Tate’s thesis: Or is it Fourier analysis on groups? There is certainly an abundance of advanced books on Galois representations and automorphic forms.

Also, when you say “not just as functions on GL2 R but rather automorpbic GL2 A ,” does that mean that given a modular form in the standard sensethere is a corresponding function on GL2 A? Harmonic Analysis in Phase Space.