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- Richard Taylor, Andrew Wiles
- 1995

- Richard Taylor
- 2006

To John Coates on the occasion of his 60 th birthday, with much gratitude. Abstract. We prove that the L-function of any regular (distinct Hodge numbers), irreducible, rank two motive over the rational numbers has meromorphic continuation to the whole complex plane and satisfies the expected functional equation.

- Christophe Breuil, Brian Conrad, Fred Diamond, Richard Taylor
- 2001

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)

- Brian Conrad, Fred Diamond, Richard Taylor
- 1999

- Barry Mazur, Laurent Clozel, Michael Harris, Richard Taylor, Nicholas Shepherd-Barron, I Thank +6 others
- 2007

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)

- Richard Taylor
- 2008

I am writing a Farsi (Persian) interpreter which uses a subset of Farsi personal-reference verb equivalents to cause changes in CPU activity. Any physically possible command to the computer is executed, according to the constraints implied by the command.

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