Search

19 Jan 2013: f(z) =a(z z0) bc(z z0) d. ,. for some a,b,c,d,z0 C. ... Nm,n=0. am,nf(z)mg(z)n 0, for some am,n C. Hence show that any two meromorphic functions f,g on a complextorus C/Λ are ‘algebraically

6 Feb 2013: By considering f (x) = g(x) x, orotherwise, show that there is some c in [0, 1] such that g(c) = c. ... 13. Let f : R R be a function that has the intermediate value property: if f (a) < c < f (b)then c = f (x) for some x between a and b.

20 Feb 2013: By using a second-order mean value theorem for f , show that φ′(x) = f ′′(θx)/2 for some. ... there is some c with a < c < b and f ′(c) = z.

26 Feb 2013: Thefinal three require some Galois Theory. 13. Let K be a number field. ... If pOL = OLthen we can write xi =. aijxj for some aij p.] Deduce that if a and b are ideals.

11 Jun 2013: Again this mypersonal view, some of my colleagues disagree.). 14 What is STEP? ... Part B) and the probability (Part C) and some will havedone neither.

13 Aug 2013: of (99) and equation (101) intoterm 2 leading to some cancellations. ... holds for some constant C if and only if. B := supa<x<b.

20 Feb 2013: For every isomorphism ι : Ql = C, the image of the residual representation rι(π′) contains SL2(Flb),up to conjugation, for some b a. • ... This contradiction shows that rι(π′) must in fact have residual imagecontaining SL2(Flb), some b a, and

12 Sep 2013: for some deformable R-algebra A, [3, Corollary 3.7] tells us that Gr(B) can becomputed as follows:. ... i. i! (b) = 0 for some i > 1. by Lemma 4.1(b).

21 Apr 2013: 4. We can get round this in the usual way(cf. part (b) proof of [11, 5.2]): take X = X′ = X(3) for some auxiliary integerN 3, and define ... If p 1 mod 3, then for some αp Zp (ordp(αp) = 2).

3 Apr 2013: element. Example. We illustrate some of the concepts introduced so far in the case where G is a split adjoint groupof type A2r. ... We begin with some generalconsiderations, and reduce to a case by case calculation using the invariant degrees of G.