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.
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 , combined with Richard Taylor's most recent , which… (More)
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.