Submitted by ims_edit on Thu, 08/03/2023 - 11:41
preprint-id:
ims23-01
preprint-title:
Böttcher coordinates at wild superattracting fixed points
preprint-abstract:
Let p be a prime number, let g(x)=xp2+pr+2xp2+1 with r∈ℤ≥0, and let ϕ(x)=x+O(x2) be the Böttcher coordinate satisfying ϕ(g(x))=ϕ(x)p2. Salerno and Silverman conjectured that the radius of convergence of ϕ−1(x) in ℂp is p−p−r/(p−1). In this article, we confirm that this conjecture is true by showing that it is a special case of our more general result.
preprint-year:
2023