An elementary introduction to the Langlands program

@article{Gelbart1984AnEI,
  title={An elementary introduction to the Langlands program},
  author={Stephen Samuel Gelbart},
  journal={Bulletin of the American Mathematical Society},
  year={1984},
  volume={10},
  pages={177-219}
}
  • S. Gelbart
  • Published 1 April 1984
  • Economics
  • Bulletin of the American Mathematical Society
Preface 
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138 Citations
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Background Citations
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Methods Citations
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Results Citations
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138 Citations

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Preface
Stable Conjugacy: Definitions and Lemmas
The purpose of the present note is to introduce some notions useful for applications of the trace formula to the study of the principle of functoriality, including base change, and to the study of…
ON AN EXPLICIT CONSTRUCTION OF A CERTAIN CLASS OF AUTOMORPHIC FORMS.
Introduction. In modern terms the problem of construction of autoniorphic functions can be expressed most elegantly in terms of representations of adele groups as the problem of obtaining the…
Linear Algebraic Groups
Algebraic geometry affine algebraic groups lie algebras homogeneous spaces chracteristic 0 theory semisimple and unipoten elements solvable groups Borel subgroups centralizers of Tori structure of…
On Shimura’s Correspondence for Modular Forms of Half-Integral Weight
G. Shimura has shown how to attach to each holomorphic cusp form of half-integral weight a modular form of even integral weight. More precisely, suppose f(z) is a cusp form of weight k/2, level N,…
Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series
In The following lectures we shall give a brief sketch of some representative parts of certain investigations that have been undertaken during the last five years. The center of these investigations…
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1. Introduction. It had been my intention to survey the problems posed by the study of zetafunctions of Shimura varieties. But I was too sanguine. This would be a mammoth task, and limitations of…
The arithmetic theory of algebraic groups
CONTENTS Introduction ??1. Arithmetic groups ??2. Ad?le groups ??3. Tamagawa numbers ??4. Approximations in algebraic groups ??5. Class numbers and class groups of algebraic groups ??6. The genus…
The action of complex conjugation on a Shimura variety
In the case that a Shimura variety has a real canonical model, complex conjugation defines an involution of the set of complex points of the variety. It is necessary to have an explicit description…
Automorphic forms on Adele groups
This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of…
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