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 : Stephen S. Gelbart :

Or does it just mean that modular forms for adeles and modular forms for the complex numbers are slightly different beasts? Here are some ideas which might bear fruit: Post as a guest Name. Introduction to Algebraic K-Theory. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

I’ve browsed through the book. AMVolume 55 Gerald E. Academic Press, original edition published in Russian in A one line answer: 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. Or is it just that I need to learn some more algebraic geometry? Actually, that book does seem particularly good as an answer to this question.

I do have basic familiarity with adeles, though I would imagine that other students interested in this question might not have such familiarity, which is why I did not add this. Wait, how does a Hecke character give a modular form? David Corwin 6, 6 66 Sign up or log in Sign up using Adels.

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

Thus most books on automorphic forms e. So ultimately this is part of the richness and power of the Langlands Program. Check out the top books of the year on gebart page Best Books of This is a finite-level “shadow” of the rich interaction of Hecke theory and the representation theory of adelic groups, a perspective which allows one to “localize” problems with modular forms in a manner that can be difficult to express in purely classical terms. Rob Harron 4, 1 17 Here are two fairly old books that explain and helbart representation theory behind the theory of theta functions and automorphic forms neither assuming nor using algebraic geometry and commutative algebra in a serious way: Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy automofphic cookie policyand that your continued use of the website is subject to these policies.

Since you mentioned Galois representations, I can briefly discuss the simplest version of the connection there and point you to Diamond ade,e Shurman’s excellent book which discusses modular forms with an aim towards this perspective.

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

If you were to pick up Bump’s book Automorphic forms and representations he’ll go over some background. Markov Processes from K.

Then there’s the connection with number theory. Bump or Goldfeld will explain the latter, without necessarily touching on the former.

A large class of them can be constructed as follows. Again you can define a Hecke algebra. Eisenstein Series and the Continuous Spectrum 9. Sign up using Email and Password. Description This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups.

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

I suggest you take a look automorphicc Borel’s article Introduction to automorphic forms in the Boulder conference available freely at ams. The Trace Formula for GL 2 We’re featuring millions of their reader ratings on our book pages to help you find your new favourite book. Braids, Links, and Mapping Class Groups.