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Galois representations, automorphic forms, and the Sato-Tate Conjecture

Author

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  • Michael Harris

    (Université Paris 7)

Abstract

The present text consists of notes of several lectures on the proof of the Sato-Tate Conjecture given up through 2008. The goal of the lectures was to explain the statement and the main ideas of the proof. The notes are somewhat dated; shortly after they were written, the author, together with Bernet-Lamb, Geraghty, and Taylor, were able to prove the analogue of the Sato-Tate conjecture for all elliptic modular forms. In particular, Theorems 2.4 and 2.5 are not conditional, and the condition on the j-invariant in Theorem 1.1 is superfluous. Moreover, the methods of proof outlined in sections 3 and 4 have been generalized and extended in a number of ways, notably in a series of articles by Barnet-Lamb, Gee, Geraghty, and Taylor, by Thorne, and by Calegari and Geraghty.

Suggested Citation

  • Michael Harris, 2014. "Galois representations, automorphic forms, and the Sato-Tate Conjecture," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(5), pages 707-746, October.
    • Handle: RePEc:spr:indpam:v:45:y:2014:i:5:d:10.1007_s13226-014-0085-4
    DOI: 10.1007/s13226-014-0085-4
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