Characterization of 2-ramified power series

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• 作者：Jonas Fransson ^{jonas.fransson@lnu.se}
• 关键词：Lower ramification numbers ; Iterations of power series ; Difference equations ; Arithmetic dynamics
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：174
• 期：Complete
• 页码：258-273
• 全文大小：323 K
• 卷排序：174

文摘

In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics p. Let g be such a series, then g has a fixed point at the origin and the corresponding lower ramification numbers of g are then, up to a constant, the degree of the first non-linear term of p-power iterates of g. The result is a complete characterization of power series g   having ramification numbers of the form 2(1+p+…+pn)2(1+p+…+pn). Furthermore, in proving said characterization we explicitly compute the first significant terms of g at its pth iterate.