Finite order automorphisms of the ring of power series over a finite field

Jakub Byszewski (Jagellonian University)

19-Oct-2020, 11:15-12:15 (3 years ago)

Abstract: The Nottingham group at a prime $p$ is the group of (formal) power series $t+a_2 t^2+ a_3 t^3+ \cdots$ in the variable $t$ with coefficients $a_i$ from the field with $p$ elements with the group operation given by composition of power series. This group is known to contain elements of order being an arbitrary power of $p$. Elements of order $p$ have been classified by Klopsch and have a nice description. For higher orders, however, only a handful of examples have been known explicitly.

In the talk we will show how to describe such series in closed computational form through finite automata. This allows us to construct many explicit examples and formulate a number of questions. The talk is based on joint work with Gunther Cornelissen and Djurre Tijsma.

number theory

Audience: researchers in the topic


Warsaw Number Theory Seminar

Organizers: Jakub Byszewski*, Bartosz Naskręcki, Bidisha Roy, Masha Vlasenko*
*contact for this listing

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