A lower bound on the canonical height for polynomials
We prove a lower bound on the canonical height associated to polynomials over number fields evaluated at points with infinite forward orbit. The lower bound depends only on the degree of the polynomial, the degree of the number field, and the number of places of bad reduction.
Mathematics Subject Classification11G50 37P30 37P45 37P15
I would like to thank Laura DeMarco for introducing me to the trees in  and , and for many helpful and enlightening discussions on that topic. I would also like to thank Patrick Ingram for several fruitful conversations on this research problem, and for sharing his results concerning the normal form used throughout this article. Finally, it is a pleasure to thank Laura DeMarco and Joseph Silverman for their useful comments on an earlier draft, and the anonymous referee for his or her careful reading and additional suggestions.
- 6.DeMarco, L.: Finiteness for degenerate polynomials. In: Lyubich, M., Yampolsky, M. (eds.) Holomorphic Dynamics and Renormalization: A Volume in Honour of John Milnor’s 75th Birthday, vol 53, pp. 89–104. Fields Institute Communications, AMS, Toronto (2008)Google Scholar