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Henry Wilton
https://www.dpmms.cam.ac.uk/~hjrw2/research.html24 Nov 2016: This page was last updated on 24 November 2016. Based on a design by Joel Fine. -
Modular forms (Lent 2016) — example sheet #2 1. ...
https://www.dpmms.cam.ac.uk/~ajs1005/modular/2015-16/ex-sheet-2-2016.pdf10 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. -
Lent Term 2016 O. Randal-Williams IB Groups, Rings, and ...
https://www.dpmms.cam.ac.uk/~or257/teaching/IBGRM/Sheet3.pdf15 Feb 2016: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4. -
PART II REPRESENTATION THEORYSHEET 2 Unless otherwise stated, all ...
www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2015-2016/repex2.pdf6 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. -
Analysis of Partial Differential Equations Example sheet 3 (Chapter…
https://www.dpmms.cam.ac.uk/~md384/example_sheet_PDE_3-v3.pdf11 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 -
C:/Users/rdc26/Desktop/coding_and_crypt-16-2 (1).dvi
www.dpmms.cam.ac.uk/study/II/Coding/2015-2016/CC2-2016.pdf15 Feb 2016: 24) Let 0 < δ < 1/2 and write. α(δ) = lim supn. -
Modular forms (Lent 2016) — example sheet #1 1. ...
https://www.dpmms.cam.ac.uk/~ajs1005/modular/2015-16/ex-sheet-1-2016.pdf2 Feb 2016: π2. 3. (1 24. n=1. σ1(n)qn. ). Explain why G2(τ) is not a modular form of weight 2. -
Lent Term 2016 O. Randal-Williams IB Groups, Rings, and ...
www.dpmms.cam.ac.uk/study/IB/GroupsRings%2BModules/2015-2016/grm20163.pdf15 Feb 2016: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4. -
Groups Example Sheet 2Michaelmas 2016 Julia Goedecke Please send ...
www.dpmms.cam.ac.uk/study/IA/Groups/2016-2017/GroupsSheet2-2016.pdf26 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. -
4 L-series Γ-function and Mellin transform Recall: Γ(s) = ...
https://www.dpmms.cam.ac.uk/~ajs1005/modular/2015-16/notes-2016-3.pdf26 Feb 2016: at least formally). 24. Example: let f(τ) =. n=1 eπin2τ. Then. -
3 Hecke operators Let L be the free abelian ...
https://www.dpmms.cam.ac.uk/~ajs1005/modular/2015-16/notes-2016-2.pdf13 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. -
VISUALISING ELEMENTS OF ORDER 7 IN THETATE-SHAFAREVICH GROUP OF ...
https://www.dpmms.cam.ac.uk/~taf1000/papers/visible7.pdf18 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. -
SUP.dvi
https://www.dpmms.cam.ac.uk/~twk10/SUP.pdf18 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 -
Modular forms part III — lecture notes A J ...
https://www.dpmms.cam.ac.uk/~ajs1005/modular/2015-16/notes-2016-1.pdf23 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 -
ICM-Proceedings-example2.dvi
https://www.dpmms.cam.ac.uk/~md384/ICMarticleMihalis.pdf3 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]. -
On the GLn-eigenvariety and a conjecture of Venkatesh David ...
https://www.dpmms.cam.ac.uk/~jat58/hwonf.pdf28 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 -
Automorphy of some residually S5 Galois representations…
https://www.dpmms.cam.ac.uk/~jat58/quintic.pdf27 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. -
A FORMULA FOR THE JACOBIAN OFA GENUS ONE CURVE ...
https://www.dpmms.cam.ac.uk/~taf1000/papers/jacobians.pdf18 Aug 2016: 24 TOM FISHER. Proposition 9.5. Suppose n 2r 1. Let D = P1. -
Arithmetic invariant theory and 2-descent for plane quartic curves ...
https://www.dpmms.cam.ac.uk/~jat58/plane_quartics.pdf29 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 -
Inverse Problems in Geometry and DynamicsLecture notes Will J. ...
https://www.dpmms.cam.ac.uk/~gpp24/ipgd(3).pdf30 Apr 2016: will introduce later (see Exercise 3.24). ... EXERCISE 1.24. Prove the lemma (the reader may find a proof using local coordinates in [GHL04,Theorem 2.124], or an intrinsic proof is given in [Pat99, Proposition 1.21], -
A 2-adic automorphy lifting theorem for unitary groups over ...
https://www.dpmms.cam.ac.uk/~jat58/p_equals_2.pdf16 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 -
Part III Computability and Logic: 24 Lectures in Michaelmas ...
https://www.dpmms.cam.ac.uk/~tef10/cam_only/partiiicomputability.pdf18 Jun 2016: 24. 2.7.2 Bounded Character. 27. 2.8 Ordinals. 28. 2.8.1 Rank functions. ... D-finite subsets. 24 CHAPTER 2. RECURSIVE DATAYPES. 2.7 Finite vs Bounded vs Unbounded Character. -
The Effective Topos J.M.E. HylandDepartment of Pure Mathematics,…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Pub81-90/hyland-effectivetopos.pdf25 May 2016: The Effective Topos. J.M.E. HylandDepartment of Pure Mathematics, Cambridge, England. 0 IntroductionThe subject of this paper is the most accessible of a series of toposes whichcan be constructed from notions of realizability: it is that based on -
The Effective Topos J.M.E. HylandDepartment of Pure Mathematics,…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Oldpapers/hyland-effectivetopos.pdf25 May 2016: The Effective Topos. J.M.E. HylandDepartment of Pure Mathematics, Cambridge, England. 0 IntroductionThe subject of this paper is the most accessible of a series of toposes whichcan be constructed from notions of realizability: it is that based on
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