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

Mueller, Julia

doi:10.1090/bull/1609

On the genesis of Robert P. Langlands’ conjectures and his letter to André Weil
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Bull. Amer. Math. Soc. 55 (2018), 493-528 Request permission

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.

References

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, DOI 10.1007/BFb0070263
R. P. Langlands, Problems in the theory of automorphic forms, Lectures in modern analysis and applications, III, Lecture Notes in Math., Vol. 170, Springer, Berlin, 1970, pp. 18–61. 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