Random Matrix Theory and central vanishing of L-functions

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  1. Topics for discussion
    1. $c_E$, the predicted constant in the frequency of rank two in the family of quadratic twists of $E$
    2. Frequency of rank 3 in a family of quadratic twists of a fixed elliptic curve
    3. Quadratic twists for higher weight forms
    4. Twists of elliptic curve L-functions by cubic and higher order characters
    5. Extremely large ranks
    6. Real quadratic twists
    7. Siegel Modular forms
    8. Zero statistics near the central point
  2. Background information
    1. Quadratic twists
    2. Imaginary quadratic twists
      1. Weight 2, Level 11
    3. Brumer's upper bound for the rank
  3. Links to data
    1. Tornaria/Rubinstein data for vanishing, thousands of curves
    2. Second order vanishing for real quadratic twists of the weight 4 level 7 Hecke cuspform
    3. Rank one quadratic twists, Delaunay and Roblot
    4. Watkin's lists of twists with odd ranks at least 3
    5. Vanishing for twists by $d \equiv 0$ modulo $p$
    6. Second order vanishing of higher order twists (Fearnley and Kisilevsky)
    7. Cubic twist of the L-function of $E$ over a quadratic extension (Watkins)
    8. Coefficients for the first few spinor zeta-functions (by Kuss)
    9. Computing the analytic rank (program from S.J. Miller)
  4. Notes from the Banff workshop
  5. Proceedings, papers and reviews
    1. Proceedings of the Newton Institute workshop on RMT and ranks of elliptic curves
    2. Frequency of order two vanishing of quadratic twists (Conrey, Keating, Rubinstein, and Snaith)
    3. Frequency of order two vanishing of cubic twists (David, Fearnley, Kisilevsky)
    4. Frequency of order 3 vanishing in the family of quadratic twists of a fixed elliptic curve (Watkins)
    5. Zero statistics (Miller, Duenez)
    6. Regulators of rank 1 curves in a family of quadratic twists (Delaunay, Roblot)
    7. Vanishing of quadratic twists of symmetric power L-functions (Watkins)
    8. Siegel Modular Forms, including several expository papers, and a book
    9. Symmetric cube L-functions as spinor zeta-functions (Schulze-Pillot)