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2. Conjugacy Invariants

    1. Problem 2.1.

      [Nigel Boston] Is Pink’s generating function $\Phi_w$ always rational for every $\rho(\text{Frob}_p)=w?$
        1. Remark. Suggestion: Try matching data to degree $1$ rational functions.
            • Problem 2.2.

              Cook up other conjugacy invariant things.
                1. Remark. List of existing and future possible ones:
                  • Markov process
                  • partitions
                  • representation of wreath products (Silverman and Levy)
                  • Generalization of cycle type (Harron)

                      Cite this as: AimPL: The Galois theory of orbits in arithmetic dynamics, available at http://aimpl.org/galarithdyn.