Open Questions: The Langlands Program
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See also: Number theory 
Algebraic number theory

Langlands program
 Article from
Wikipedia.

The work of Robert Langlands
 This is an archive of many of Langlands' papers and writings,
which indicates the general topics of concern in his "program".
Most documents are available in downloadable format.

The Langlands Program
 One paragraph summary by Harry Riesmann.
 Harmonic Analysis and Group Representations
James Arthur
Notices of the AMS, January 2000, pp. 2634
 The Langlands program is a way of organizing number theoretic
data in terms of analytic objects. This survey paper explains it
in terms of HarishChandra's fundamental work on representation
theory.
[Article in PDF format]
 The Nonabelian Reciprocity Law for Local Fields
Jonathan Rogawski
Notices of the AMS, January 2000, pp. 3541
 Reciprocity laws in number theory are farreaching generalizations
of the quadratic reciprocity law in elementary number theory, which
specifies when "square roots" modulo a prime exist. This research
paper explains how the Langlands program yields a generalized
reciprocity law for matrices over a padic field.
[Article in PDF format]
 On some applications of automorphic forms to number theory
Daniel Bump; Solomon Friedberg; Jeffrey Hoffstein
Bulletin of the AMS, April 1996, pp. 157175
 The basic idea of Dirichlet series is to study an interesting
sequence of numbers by means of investingating analytic properties
of the Dirichlet series having the numbers as coefficients. Part of
the Langlands program is to make general statements about such
series. The present paper deals with a generalization in which
the coefficients themselves are functions of a complex variable.
[Abstract, references, downloadable text]
 Group Representations and Harmonic Analysis from Euler to
Langlands, Part II
Anthony W. Knapp
Notices of the AMS, May 1996, pp. 537549
 Group representations provide a mechanism for generalizing
harmonic analysis to deal with nonabelian groups. This generalized
theory is fundamental to the Langlands program, and is applicable
in many other areas as well, such as the theory of Lie groups.
[Article in PDF format]
 Group Representations and Harmonic Analysis from Euler to
Langlands, Part I
Anthony W. Knapp
Notices of the AMS, April 1996, pp. 410415
 Group representations and harmonic analysis play a central
role in the Langlands program. The two topics have applications
as diverse as number theory, probability, and mathematical
physics. The origins of the main ideas
can be found in the work of Euler, Fourier, and Dirichlet.
[Article in PDF format]
 Selberg's Conjectures and Artin's Lfunctions
M. Ram Murty
Bulletin of the AMS, July 1994, pp. 114
 Nonabelian reciprocity laws can be expressed as an identity
between Lfunctions defined in different ways. In 1989 Atle
Selberg stated some conjectures about complex functions having
properties typical of Lfunctions. The relationship of
these conjectures to the Langlands program is discussed.
 An Elementary Introduction to the Langlands Program
Stephen Gelbart
Bulletin of the AMS, 10(1984), pp. 177219
 The essence of the Langlands conjecture is that the possible
number fields of degree n are related to and constrained by
the irreducible infinite dimensional representations of GL(n).
How automorphic forms and Lfunctions help provide the connection
is explained in this excellent survey paper.
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