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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In particular, Jacobi sums come up in both number theory and representation theory and quadratic forms then relate to theta functions. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections auomorphic the classical theory.

Since the action is associative, i.

The Calculi of Lambda Conversion. We’re featuring millions of their reader ratings on our book pages to help you find your new favourite book. I have a solid background knowledge at the first-year graduate level I’ve passed qualsbut I don’t know what the prerequisites for Gelbart’s book are.

Automorphic Forms on Forma Groups. As for suggestions on what to read, I found Gelbart’s book Automorphic forms autoomrphic adele groups pretty readable. Braids, Links, and Mapping Class Groups. This gives a representation.

Is it Lie theory and if so what aspects of it? Eisenstein Series forsm the Continuous Spectrum 9. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge foorms you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. 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.


To be a bit more descriptive about my background: AMVolume 82 Joan S. Automorphic Forms on a Quaternion Algebra show more. David Corwin 6, 6 66 Academic Press, original edition published in Russian in Lion, Vergne, The Weil representation, Maslov index and theta series.

Tate’s thesis gives a proof of the functional equation for the associated L-functions purely in terms of representation theory. Hecke Theory for GL 2 7. Here, too, the results from representation theory can be translated back into information about theta functions. In addition, Hecke operators are symmetric-like sums over elements of groups, which would suggest a strong connection to representation theory.

AMVolume 51 John Milnor.

Home Questions Tags Users Unanswered. AMVolume AMVolume Vladimir Voevodsky.

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

To answer the question in your second comment I’ll say this: By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. I think I yroups to go to bed now. It’ll give you a bit of an idea of the type of thing that goes into simply the definition of an automorphic form.

Home Contact Us Help Free delivery worldwide. Such as, giving a source or writing a small exposition? This is a substitute for the group ring that occurs in the representation theory of finite groups, i. 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.

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

One of my ideas might be fruitful, or they all might have nothing to do with why representation theory connects to modular functions. This is explained in detail in Automorphic forms on adele groups by Gelbart. Sign up or log in Sign up using Google.


Academic Press, original edition published in Russian in It’s really a vast subject and I didn’t learn from any one or few sources. AMVolume Amnon Neeman. Cycles, Transfers, and Motivic Homology Theories. It is a pity that things like these don’t occur in complex analysis courses.

A one line answer: 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. For details, I’d refer you to any one of the books I suggested. There is certainly an abundance of advanced books on Galois representations and automorphic forms. 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.

But I think your comment 3 is implying that it’s in analogy with L-functions of Hecke characters, not that the latter are actually automorphic forms of some kind. Dispatched from the UK in 4 business days When will my order arrive?

What is the basic connection between modular forms and representation 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. I haven’t taken a course in representation theory beyond representations of finite groups and would be interested in knowing where I can get the required representation theory background before reading the book.