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Modular forms and L-functions (Michaelmas 2019) — example sheet ...
https://www.dpmms.cam.ac.uk/~ajs1005/modular/ex-sheet-4-2019.pdf28 Nov 2019: 4. Let E2(z) = 1 24. n=1 σ1(n)qn = (3/π2)G2(z) as in sheet 2, Q8. -
Lossless Compression with Moderate Error Probability
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/MDP.pdf5 Jun 2020: Previous work along theselines has been described in [24]–[29]. These studies reportthat error probability vanishes sub-exponentially fast, and theycharacterize the rate of this decay. ... 24] J. Chen, D.-k. He, A. Jagmohan and L. A. Lastras-Montaño, -
Estimating the Entropy Rate of Spike Trains Yun GaoDiv. ...
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/spikes-CISS.pdf5 Jun 2020: In-form. Theory, 24:530–536, 1978. 3. -
The ODE Method and Spectral Theory of Markov Operators ...
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/hkm.pdf5 Jun 2020: Sadhana, 24(4-5):425{452, 1999. Chance as necessity. 8. V.S. Borkar and S.P. ... Sadhana, 24(4-5):369{423, 1999. Chance as necessity. 16. S.V. Hanly and D. -
Example sheet 3, Galois Theory, 2021 1. Let M/K ...
https://www.dpmms.cam.ac.uk/study/II/Galois/2021-2022/ex3_2021.pdf15 Oct 2021: Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}. -
Spaces of manifolds
https://www.dpmms.cam.ac.uk/~or257/slides/Princeton2022.pdf13 Apr 2022: 40. 42. 44. 46. 48. 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 -
Geometry-of-numbers over number fields and the density of ADEfamilies …
https://www.dpmms.cam.ac.uk/~mo512/nf.pdf23 May 2024: 1. 5.1 Averaging and reductions. 21. 5.2 Slicing. 24. 5.3 Congruence conditions. -
The Ward Correspondence and StationaryAxisymmetric Spacetimes…
https://www.dpmms.cam.ac.uk/~gt306/mp1.pdf16 Jan 2024: where. νabcd =1. 24. det(η)εabcd. The coordinates (w,z,w̃, z̃) are called double null coordinates. ... wγn = z̃γn1 and zγn = w̃γn1. (24). The Birkhoff factorization F = f̃1f is given by4. -
Ek-algebras and homological stability
https://www.dpmms.cam.ac.uk/~or257/slides/eCHT.pdf16 Jan 2020: Figure 1: Hd(Γg,1, Γg1,1; Q);? means unknown,? means not zero. Non-zero groups: use results of Faber, Kontsevich, Morita.24. -
Hamilton Paths in Certain Arithmetic Graphs Paul A. Russell∗† ...
https://www.dpmms.cam.ac.uk/~par31/preprints/hamilton.pdf30 Jan 2005: But what we need is simply a Hamilton path from 0to 54 in G3 [[0, 21] {24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60}], for which ... 0, 3, 1, 4, 7, 10, 13, 16, 19, 57, 60, 20, 17, 14, 11, 8, 5, 2, 6, 9, 12, 15, 18, 21,24, 27, 30, 33, 36, 39, 42,
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