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24 Nov 2016: This page was last updated on 24 November 2016. Based on a design by Joel Fine.

10 May 2016: 1. 2πi. d. dτlog (τ) = q. d. dqlog (τ) =. 3. π2G2(τ) = 1 24. n=1. σ1qn. Hence show that. (τ) = qn=1. ... 1 qn)24. 8. (Rankin-Selberg integral) Let f, g Sk(SL2(Z)), with q-expansionsanq.

15 Feb 2016: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4.

11 Nov 2016: 24). (15.a) Using an existence result from the theory of ODEs, show that for each n N there exists a uniquefunction un(t) of the form (23) satisfying (24).[Hint: ... Show that the limit function is indeed a weak solution of (20) inthe sense of (22) by

6 Jan 2016: 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2. ... 24 = g5.]. 10 Let a finite group G act on itself by conjugation.

15 Feb 2016: 24) Let 0 < δ < 1/2 and write. α(δ) = lim supn.

2 Feb 2016: π2. 3. (1 24. n=1. σ1(n)qn. ). Explain why G2(τ) is not a modular form of weight 2.

26 Oct 2016: 3. (a) Show that the symmetric group S4 has a subgroup of order d for each divisor d of 24,and find two non-isomorphic subgroups of order 4.

15 Feb 2016: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4.

26 Feb 2016: at least formally). 24. Example: let f(τ) =. n=1 eπin2τ. Then.

13 Feb 2016: 144169)(x 540 12. 144169). 22. (144169 is prime). In particular we see that the Hecke eigenforms of weight 24 donot have rational coefficients.

18 Oct 2016: In the third year studentshave supervisions in specific subjects (generally 4 supervisions for a 24 hourcourse and 3 supervisions for a 16 hour course). ... Be Specific I was once told by a Swimming Trainer that it took 24 hoursof training to modify a

18 Aug 2016: Inparticular L has degree 24, and its only non-trivial subfield has degree 8. ... Let L be the number field of degree 24 defined by the x-coordinate of a 7-torsion.

23 Feb 2016: Modular forms part III — lecture notes. A J Scholl1. These are the notes from 2008 with corrections and edited to reflect better thecontent and presentation of the course in 2016. 1 Elliptic functions. Generalities. Function theory on an elliptic

3 Feb 2016: See [11, 72] for the original treatments and also [24]. The expectation that the Kerr solutions are unique even without imposingaxisymmetry stems from a pretty rigidity argument due to Hawking [47].

27 Apr 2016: 9 Deduction of the main theorem 24. 1 Introduction. Let F be a totally real number field, let p be a prime, and let ρ : GF GL2(Qp) be a geometric ... 5.24]) one can find a Taylor–Wiles set Q1 with the required properties.

28 Nov 2016: On the GLn-eigenvariety and a conjecture of Venkatesh. David Hansen and Jack A. Thorne†. November 28, 2016. Abstract. Let π be a cuspidal, cohomological automorphic representation of GLn(A). Venkateshhas suggested that there should exist a

18 Aug 2016: 24 TOM FISHER. Proposition 9.5. Suppose n 2r 1. Let D = P1.

29 Apr 2016: 23A.3 Proof of Proposition A.2. 24. Introduction. Motivation. Let C be a smooth, projective, geometrically connected algebraic curve over a field k ofcharacteristic 0, and let J denote its

16 Mar 2016: A 2-adic automorphy lifting theorem for unitary groups over CM. fields. Jack A. Thorne. March 16, 2016. Abstract. We prove a ‘minimal’ type automorphy lifting theorem for 2-adic Galois representations of unitarytype, over imaginary CM fields. We