# The density of prime divisors in the arithmetic dynamics of quadratic polynomials

@article{Jones2008TheDO, title={The density of prime divisors in the arithmetic dynamics of quadratic polynomials}, author={Rafe Jones}, journal={Journal of The London Mathematical Society-second Series}, year={2008}, volume={78}, pages={523-544} }

Let f [x], and consider the recurrence given by an = f(an � 1), with a0 . Denote by P(f, a0) the set of prime divisors of this recurrence, that is, the set of primes dividing at least one non-zero term, and denote the natural density of this set by D(P(f, a0)). The problem of determining D(P(f, a0)) when f is linear has attracted significant study, although it remains unresolved in full generality. In this paper, we consider the case of f quadratic, where previously D(P(f, a0)) was known only… Expand

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