The Density of Primes in Orbits of zd+c

@article{Hamblen2013TheDO,
  title={The Density of Primes in Orbits of zd+c},
  author={Spencer Hamblen and Rafe Jones and K. Jeevan Madhu},
  journal={International Mathematics Research Notices},
  year={2013},
  volume={2015},
  pages={1924-1958}
}
  • Spencer Hamblen, Rafe Jones, K. Jeevan Madhu
  • Published 2013
  • Mathematics
  • International Mathematics Research Notices
  • Given a polynomial f(z) = z^d + c over a global field K and a_0 in K, we study the density of prime ideals of K dividing at least one element of the orbit of a_0 under f. The density of such sets for linear polynomials has attracted much study, and the second author has examined several families of quadratic polynomials, but little is known in the higher-degree case. We show that for many choices of d and c this density is zero for all a_0, assuming K contains a primitive dth root of unity. The… CONTINUE READING

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