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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Description This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. More importantly, I have a basic background in the representation theory of finite groups.

To be a bit more descriptive about my background: 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? AMVolume Michael Harris.

Back cover copy The subject matter of these Notes is the interplay between the theory of automorphic forms and group representations. Sign up using Email and Password.

To answer the question in your second comment I’ll say this: This goups quite appropriate. Sign up using Facebook. Or is it just that I need to learn some more algebraic geometry? What is the basic connection between modular forms and representation theory? Email Required, but never shown. 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.

Post as a guest Name. Since the action is associative, i. The pn equation can be seen as an adelic version of the Poisson summation formula. AMVolume 59 David Mumford. This type of stuff is the basic connection of modular forms to representation theory and it goes back at least to Gelfand—Graev—Piatestkii-Shapiro’s Representation theory and automorphic functions. Looking for beautiful books?

Progress in Mathematics, 6. Interpreting important automoprhic contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences gelbadt connections with the classical theory. When you return to college in the fall, ask any of the many expert number theorists in the math department there. To get into the Langlands program there’s the book an introduction to the Langlands program google books you could look at.

Dynamics in One Complex Variable. I also added “reference request” because I imagine there might be a text which is at my level and discusses these ideas.

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

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

Here are two fairly old books that explain and exploit representation theory behind the theory of theta functions and automorphic gropus neither assuming nor using algebraic geometry and commutative algebra in a serious adepe.

Pretty much the only way to take an automorphic representation and prove that it has an associated Galois representation is to construct a gelbzrt 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. The underlying theme is the decomposition of the regular representation of the adele group of GL 2. Sign up or log in Sign up using Google.

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. AMVolume 51 John Milnor. The right point of view is that the right regular representation decomposes into irreducible representations.

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

Lectures on Curves on an Algebraic Surface. One remark how I think about Tate’s thesis: 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 function on adeles.

So ultimately this is part of the richness and power of the Langlands Program. This fits into another part of the Langlands program which is the functoriality conjectures really the correspondences are special dorms. David Corwin 6, 6 66 Wait, how does a Hecke character give a modular form? Harmonic Analysis in Phase Space. Grkups right regular representation on an locally compact abelian groups is in direct connection with its Fourier transform.

AM-7Volume 7 Paul R. Check out the top books of the year on our page Best Books of Then there’s the connection with number theory. Throughout the work the author emphasizes new examples and problems that remain open within the general theory.