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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The functional equation can be seen as an adelic version of the Poisson summation formula.
Automorphic Forms on Adele Groups. (AM-83), Volume 83
AMFroups 76 John Milnor. I suggest you take a look at Borel’s article Introduction to automorphic forms in the Boulder conference available freely at ams. When you return to college in the fall, ask any of the many expert number theorists in the math department there. Progress in Mathematics, 6.
Automorphic Forms on Adele Groups. (AM), Volume 83 : Stephen S. Gelbart :
Here, too, the results from representation theory can be translated back into information about theta functions. Other books in this series. This is a substitute for the group ring that occurs in the representation theory of finite groups, i.
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The underlying theme is the decomposition of the regular representation of the adele group of GL 2. Apurv 2, 16 Groupz also added “reference request” because I imagine there might be a text which is at my level and discusses these ideas.
Check out the top books of the year on our page Best Books of What kind of math do you need to know to do these books? This fits into another part of the Langlands program which is the functoriality conjectures really the correspondences are special cases.
How is representation theory used in modular/automorphic forms? – MathOverflow
Home Contact Us Help Free delivery worldwide. We’re featuring millions of their reader ratings on our book pages to help you find your new favourite book. One of my ideas might be fruitful, or they all might have nothing to do with why representation theory connects to modular functions.
Pretty much the only way to take an automorphic representation and prove that it has an associated Galois representation aktomorphic to construct a geometric object whose cohomology has both an action of the Hecke algebra and the Galois group and froups it into pieces and pick out the one you want.
Home Questions Tags Users Unanswered. AM-7Volume 7 Paul R. Probably the most notable example is aitomorphic moonshine. As you probably know, the real and imaginary parts of a holomorphic function are harmonic, i.
Such as, giving a source or writing a small exposition? More importantly, I have a basic background in the representation theory of finite groups. Well automorphoc basic link to representation theory is that modular forms and automorphic forms can be viewed as functions in representation spaces of reductive groups. AMVolume These correspondences should be nice in that adel that happen on one side should correspond to things happening on the other. Or is it Fourier analysis on groups?
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The Trace Formula for GL 2 Since the action is associative, i. You might also be interested in this survey article by Darmon, Diamond, and Taylor: Automorphic Forms on Adele Groups.
An introduction to the Langlands program by Bernstein and others is also good. The Best Books of Gelfand, Graev, Piatetskii-Shapiro, Representation theory and automorphic functions.
The point of listing ideas is to show the kind of intuition I might be looking for. AMVolume 82 Joan S. The most comprehensive reference is the Corvallis proceedings available freely at ams. AMVolume Edward Nelson.
This is explained in detail in Automorphic forms on adele groups by Gelbart. The right point of view is that the right regular representation decomposes into irreducible representations. Sign up using Facebook. 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.
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.