On the genesis of Robert P. Langlands' conjectures and his letter to André Weil

Author:
Julia Mueller

Journal:
Bull. Amer. Math. Soc.

MSC (2010):
Primary 11F66, 11F70, 11F80, 22E55

DOI:
https://doi.org/10.1090/bull/1609

Published electronically:
January 25, 2018

Original version:
Posted January 25, 2018.

Corrected version:
Current version clarifies inaccurate statement in Section 3.1 regarding the proof of Fermat’s Last Theorem and the final title of the author’s upcoming monograph in section 1.2 and the Acknowledgments.

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Abstract | References | Similar Articles | Additional Information

Abstract: This article is an introduction to the early life and work of Robert P. Langlands, creator and founder of the Langlands program. The story is, to a large extent, told by Langlands himself, in his own words. Our focus is on two of Langlands' major discoveries: automorphic -functions and the principle of functoriality. It was Langlands' desire to communicate his excitement about his newly discovered objects that resulted in his famous letter to André Weil. This article is aimed at a general mathematical audience and we have purposely not included the more technical aspects of Langlands' work.

- [A]
J. Arthur,
*Functoriality and the trace formula*, available at`www.math.toronto.edu/arthur/`. **[G-J]**Roger Godement and Hervé Jacquet,*Zeta functions of simple algebras*, Lecture Notes in Mathematics, Vol. 260, Springer-Verlag, Berlin-New York, 1972. MR**0342495****[L]**R. P. Langlands,*Problems in the theory of automorphic forms*, Lectures in modern analysis and applications, III, Springer, Berlin, 1970, pp. 18–61. Lecture Notes in Math., Vol. 170. MR**0302614**- [L1]
R. Langlands,
*The genesis and gestation of functoriality*. TIFR, Mumbai, Feb. 2005, available at`www.math.tifr.res.in/sites/default/files/maths/TheGenesis.pdf`. - [L2]
R. Langlands,
*Funktorialitat in der Theorie der atomotphen Formen: Ihre Entdeckung und ihre Ziele*[from a translated text], available at`http://publications.ias.edu/rpl/`. **[T]**J. T. Tate,*Global class field theory*, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 162–203. MR**0220697**

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Additional Information

**Julia Mueller**

Affiliation:
Department of Mathematics, Fordham University, 441 East Fordham Road, Bronx, New York 10458

Email:
jmueller@fordham.edu

DOI:
https://doi.org/10.1090/bull/1609

Keywords:
Eisenstein series,
spectral theory,
classical $L$-functions,
Langlands,
$L$-functions,
Galois representations,
automorphic representations,
functoriality

Received by editor(s):
November 8, 2017

Published electronically:
January 25, 2018

Article copyright:
© Copyright 2018
American Mathematical Society