Preperiodic points of polynomials over global fields
By Robert L. Benedetto. 2005
61 citations recorded by the source corpus.
Abstract Given a global field K and a polynomial defined over K of degree at least two, Morton and Silverman conjectured in 1994 that the number of K-rational pre-periodic points of is bounded in terms of only the degree of K and the degree of . In 1997, for quadratic polynomials over K = ℚ, Call and Goldstine proved a bound which was exponential in s, the number of primes of bad reduction of . By careful analysis of the filled Julia sets at each prime, we present an improved bound on the order of s log s. Our bound applies to polynomials of any degree (at least two) over any global field K.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bbc088b325d6e32d26e4a59169b94782949d2ec6
How researchers see this paper
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In Algebra and Number Theory
- Laura Demarco
- T. Tucker
- Joseph H. Silverman
- Rafe Jones
- Patrick Ingram
- Robert L. Benedetto
- Michelle Manes
- Franccois Berteloot
In Geometry and Topology
- T. Tucker
- Robert L. Benedetto
- Laura Demarco
- Joseph H. Silverman
- Michelle Manes
- Rafe Jones
- Patrick Ingram
- Franccois Berteloot
In Mathematical Physics
- T. Tucker
- Robert L. Benedetto
- Michelle Manes
- Rafe Jones
- Laura Demarco
- Patrick Ingram
- Joseph H. Silverman
- Franccois Berteloot
Citations in the corpus
- Current trends and open problems in arithmetic dynamics (2018, background): “More generally, we may consider the two-dimensional family consisting of all degree 2 rational maps of P1 defined over Q. Conjecture 4.8 (Benedetto–Chen–Hyde–Kovacheva–White, 2014, [34]; Blanc– Canci–Elkies, 2015, [39]).”