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

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

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

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.

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

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

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.

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