Richard L. Taylor

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Introduction In this paper, building on work of Wiles Wi] and of Wiles and one of us (R.T.) TW], we will prove the following two theorems (see x2.2). Theorem A. If E =Q is an elliptic curve, then E is modular. Theorem B. If : Gal(Q=Q) ! GL 2 (F 5) is an irreducible continuous representation with cyclotomic determinant, then is modular. We will rst remind(More)
Introduction Four decades ago, Mikio Sato and John Tate predicted the shape of probability distributions to which certain " error terms " in number theory conform. Their prediction—known as the Sato-Tate Conjecture—has been verified for an important class of cases thanks to the recent work of [18], combined with Richard Taylor's most recent [54], which(More)
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