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  2. ANALYSIS I EXAMPLES 4 G.P. Paternain Lent 2010 Comments ...

    https://www.dpmms.cam.ac.uk/~gpp24/aI4.pdf
    15 Feb 2010: dx log n for n N. Show that In =. 1/20. f (t/n) dt and hence that|In| < 1/9n2. By considering. ... 7. Let In = π/20. cosn x. Prove that nIn = (n 1)In2, and hence 2n2n1 I2n1/I2n 1.
  3. Hypersurfaces and the Weil conjectures

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/bogaz.pdf
    29 Jan 2010: 20 / 21. Conclusions. The proof is complicated but is mostly rather formal.
  4. STATISTICS Part IB Example Sheet 3 (of 3) RJS/Lent ...

    https://www.dpmms.cam.ac.uk/study/IB/Statistics/2009-2010/Example3.pdf
    24 Feb 2010: α (deg) 5 10 15 20 25 30 35 40 45sin 2α 0.1736 0.3420 0.5 0.6428 0.7660 0.8660 0.9397 0.9848 1range (m) 4860
  5. STATISTICS Part IB Example Sheet 2 (of 3) RJS/Lent ...

    https://www.dpmms.cam.ac.uk/study/IB/Statistics/2009-2010/Example2.pdf
    8 Feb 2010: Improved No difference WorsePlacebo 18 17 15Half dose 20 10 20Full dose 25 13 12.
  6. MODULAR FORMS AND ALGEBRAIC K-THEORY A. J. SCHOLL In ...

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/gen.pdf
    29 Jan 2010: Soulé. 20–1–1985[8] P. Deligne, M. Rapoport, Les schémas de modules des courbes elliptiques. ... In [18].[20] A. J. Scholl, The -adic representations attached to a certain noncongruence.
  7. Numbers and Sets (2010–11) Example Sheet 1 of 4 ...

    https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2010-2011/examples-NS-10-1.pdf
    19 Oct 2010: 2. Between0 and 10 there are four primes. The same is true between10 and 20.
  8. EXAMPLE SHEET 3 (LECTURES 13–18) GALOIS THEORY MICHAELMAS 2009 ...

    https://www.dpmms.cam.ac.uk/study/II/Galois/2009-2010/ex3.pdf
    28 Mar 2010: See Example Sheet 2, Problem 10.). 20. (i) Let p be prime.
  9. PART II REPRESENTATION THEORYSHEET 3 Unless otherwise stated, all ...

    https://www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2009-2010/repex3.pdf
    30 Mar 2010: Hence find the complete character table of S5. Repeat, replacing S4 by the subgroup 〈(12345), (2354)〉 of order 20 in S5.
  10. Example Sheet 3. Lectures 13–18, Galois Theory Michaelmas 2010 ...

    https://www.dpmms.cam.ac.uk/study/II/Galois/2010-2011/2010_Galois_Ex3.pdf
    9 Nov 2010: group. 3.13. Use (1) the structure of (Z/(m)) (Problem 2.20), (2) the Dirichlet’s theorem onprimes in arithmetic progressions, stating that if a and b are coprime positive ... Write cos(2π/17) explicitly in terms of radicals. 3.20. (i) Let G be a
  11. Numbers and Sets (2010–11) Example Sheet 3 of 4 ...

    https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2010-2011/examples-NS-10-3.pdf
    9 Nov 2010: Evaluate 1000! (mod 10249). 6. Without using a calculator, evaluate 20!2120 (mod 23) and 1710000 (mod 30).
  12. Example Sheet 1. Lectures 1–6, Galois Theory Michaelmas 2010 ...

    https://www.dpmms.cam.ac.uk/study/II/Galois/2010-2011/2010_Galois_Ex1.pdf
    20 Oct 2010: optional) October 20, 2010t.yoshida@dpmms.cam.ac.uk.
  13. Michaelmas Term 2010 T.A. Fisher Linear Algebra: Example Sheet ...

    https://www.dpmms.cam.ac.uk/study/IB/LinearAlgebra/2010-2011/lin_alg-10-2.pdf
    27 Oct 2010: . 1 1 00 3 20 1 0. .  ,. . . 1 1 10 3 20 1 0. .  ,. . . 1 1 11 3 11 1 1. .
  14. Hypersurfaces and the Weil conjectures

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/bristol.pdf
    29 Jan 2010: Enough to prove RH for this component. 20 / 25. I: passing to a semistable family. ... Enough to prove RH for this component. 20 / 25. II: local monodromy.
  15. Vanishing cycles and non-classical parabolic cohomologyA. J.…

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/van.pdf
    29 Jan 2010: F intertwining and. Therefore( Xx; Z; F) ' ( X0x0; Z0; F0) as required.Combining 1.20 and 1.21 gives 1.9. ... J. Scholl; On the Hecke algebra of a noncongruence subgroup. Preprint (1993)20 J.-P.
  16. A note on trilinear forms for reducible representations and ...

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/trilinear.pdf
    29 Jan 2010: The key point is that in the displayed formula in themiddle of page 20, the denominator is non-zero; it vanishes only when one of V1,V2 is isomorphic to Ind.
  17. Example Sheet 2. Lectures 7–12, Galois Theory Michaelmas 2010 ...

    https://www.dpmms.cam.ac.uk/study/II/Galois/2010-2011/2010_Galois_Ex2.pdf
    5 Nov 2010: 2.20. In this question we determine the structure of the groups (Z/(m)).(i) Let p be an odd prime.
  18. On the equivalence of binary quartics J. E. Cremona ...

    https://www.dpmms.cam.ac.uk/~taf1000/papers/quarticequiv.pdf
    12 Oct 2010: 4(cd 6be)XY 3 (3d2 8ce)Y 4,. and the sextic. g6(X, Y ) = (b3 8a2d 4abc)X6 2(16a2e 2abd 4ac2 b2c)X5Y5(8abe b2d 4acd)X4Y 2
  19. Remarks on special values of L-functions Anthony J. Scholl* ...

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/remarks.pdf
    29 Jan 2010: Soulé. 20–1–1985. [Del4] P. Deligne; Le groupe fondamental de la droite projective moins.
  20. SOME BOUNDS ON THE COEFFICIENTSOF COVERING CURVES T.A. FISHER ...

    https://www.dpmms.cam.ac.uk/~taf1000/papers/ncovbds.pdf
    29 Jul 2010: 31 λ3x. 33 x0x1x2 = 0. n = 4. {λ0x. 20 x1x3 λ2x22 = 0. ... 20 T.A. FISHER. It follows by the identity. (Aλ2µ1µ3)2(Aλ2µ. 22)(Aλ1µ2µ3). 2(Aλ1µ1µ4)2(Aλ2µ.
  21. Integral elements in K-theory and products ofmodular curves A ...

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/k1.pdf
    29 Jan 2010: We are going to show that the pullback of. τα(uα). 20 Integral elements in K-theory and products of modular curves.

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