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
One goal is to interpret some recent developments in this area, most significantly the theory of Jacquet-Langlands, working out, whenever possible, explicit consequences and connections with the classical theory. In addition, Hecke operators are symmetric-like sums over elements of groups, which would suggest a strong connection to representation theory. Yroups, when you say “not just as functions on GL2 R but rather on GL2 A ,” does that mean that given a modular gelgart in the standard sensethere is a corresponding function on GL2 A?
For details, I’d refer you to any one of the books I suggested. This is mostly encompassed under the phrase “Langlands program” and is a significantly more aytomorphic beast than the above stuff. Introduction to Algebraic K-Theory. I’m asking this in part because I imagine a number of students with similar background as I have would have learned about modular forms and thus might be interested to understand how they relate to representation theory, despite not having an extensive background in more advanced results in algebraic geometry and commutative algebra needed for advanced study in the field.
As you probably know, the real and imaginary parts of a holomorphic function are harmonic, i.
Somehow one manages to understand a bit without knowing all. Again you can define a Hecke algebra. A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this forns.
AMVolume 76 John Milnor.
Other books in this series. I’ve browsed through the book. Automorphic Forms on a Quaternion Algebra show more. But also the representation theory of reductive Lie groups both the finite-dimensional case and the infinite-dimensional case, at least the “admissible” case. AMAutoomrphic Edward Nelson. This is explained in detail in Automorphic forms on adele groups by Gelbart.
Home Contact Us Help Free delivery worldwide. Academic Press, original edition published in Russian in Gelfand, Graev, Piatetskii-Shapiro, Representation theory and automorphic functions.
Post as a guest Name. The Calculi of Lambda Conversion. Actually, that book does seem particularly good as an answer to this question.
AMVolume 82 Joan S. I also added “reference request” because I imagine there might be a text which is at my level and discusses these ideas.
In fact, my main familiarity with them is in showing the equivalence of ideal-theoretic and idelic class field theory, which is precisely your “toy version,” so I’m quite curious to eventually understand what you talked about.
Thus most books on automorphic forms e.
Automorphic Forms on Adele Groups. (AM), Volume 83 : Stephen S. Gelbart :
Bump or Goldfeld will explain the latter, without necessarily touching on the former. Such as, giving a source or writing a small exposition?
Radically Elementary Probability Theory. Here are two fairly old books that explain and exploit representation theory behind the theory of theta functions and automorphic forms neither assuming nor using algebraic geometry and commutative algebra in a serious way: Home Questions Tags Users Unanswered.
Automorphic Forms on Adele Groups. (AM), Volume 83
More importantly, I have a basic background in the representation theory of finite groups. Wait, how does a Hecke character give a modular form? A one line answer: See Bump’s book section 2. 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.
Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. To be a bit more descriptive about my background: Or is it Fourier analysis on groups? At least part of this started with Langlands classification of the admissible representation of real reductive groups.
Academic Press, original edition published in Russian in Lion, Vergne, The Weil representation, Maslov index and theta series.