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-83), Volume 83

A large class of them can be constructed as follows. Here, too, the results from representation theory can be translated back into information about theta functions.

AMVolume But velbart the representation theory of reductive Lie groups both the finite-dimensional case and the infinite-dimensional case, at least the “admissible” case. Eisenstein Series and the Continuous Spectrum 9. So ultimately this is part of the richness and power of the Langlands Program. Email Required, but never shown. Looking for beautiful books? It is a pity that things like these don’t occur in complex analysis courses.

Academic Press, original edition published in Russian in 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. Mathematics Stack Exchange works best with JavaScript enabled. Post as a guest Name. This is mostly encompassed under the phrase “Langlands program” and is a significantly more complicated beast than the above stuff.


Description This volume investigates the interplay between the classical theory of automorphic forms and the modern forjs of representations of adele groups.

Home Contact Us Help Free delivery worldwide. This gives a representation. Finite Dimensional Vector Spaces. 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.

Yes, plus other conditions such as level 1, but this would have taken up more than 1 line. There are numerous variations of this: I also added “reference request” because I imagine there might be a text which is at my level and discusses these ideas. A one line answer: What kind of math do you need to know to do these books? Such as, giving a source or writing a small exposition? Again you can define a Hecke algebra. AMVolume 51 John Milnor. MathOverflow works best with JavaScript enabled.

Other books in this series. AMVolume Amnon Neeman. Dynamics in One Complex Variable. In addition, Hecke operators are symmetric-like sums over elements of groups, which would suggest a strong connection to representation theory.

Throughout the work the author emphasizes new examples and problems that remain open within the general theory. Then there’s the connection with number theory.

This seems quite appropriate. Markov Processes from K.

I’ve browsed through the book. Automorphic Forms on a Quaternion Algebra show more. Rob Harron 4, 1 17 I think I need to go to bed now. 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 ggelbart modular forms in a manner that can be difficult to express in purely classical terms.


What I mean is the following: Academic Press, original edition published in Russian in Lion, Vergne, The Weil representation, Maslov index and theta series.

Introduction to Algebraic K-Theory. AM-6Volume 6 Alonzo Church. OfrmsVolume Vladimir Voevodsky. As for suggestions on what to read, I found Gelbart’s book Automorphic forms on adele groups pretty readable.

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

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Product details Format Paperback pages Dimensions x x Sign up using Facebook. Or is it Fourier analysis on groups? This is all with an undergraduate background in complex analysis and algebra Galois theory. Harmonic Analysis in Phase Space. From this view point, the algebraic geometry side grlups the picture enters simply as the source for proving vorms of the Langlands conjectures.

To be a bit more descriptive about my background: See Bump’s book section 2.

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