On the genesis of Robert P. Langlands’ conjectures and his letter to André Weil
Author:
Julia Mueller
Journal:
Bull. Amer. Math. Soc. 55 (2018), 493-528
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.
MathSciNet review:
3854076
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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 $L$-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.
- J. Arthur, Functoriality and the trace formula, available at www.math.toronto.edu/arthur/.
- Roger Godement and Hervé Jacquet, Zeta functions of simple algebras, Lecture Notes in Mathematics, Vol. 260, Springer-Verlag, Berlin-New York, 1972. MR 0342495
- 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
- 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.
- 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/.
- 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
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
