An arithmetic group associated with a Pisot unit, and its symbolic-dynamical representation

Nikita Sidorov

Displaying similar documents to “An arithmetic group associated with a Pisot unit, and its symbolic-dynamical representation”

On the lonely runner conjecture

Ram Krishna Pandey (2010)

Mathematica Bohemica

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Suppose $k + 1$ runners having nonzero distinct constant speeds run laps on a unit-length circular track. The Lonely Runner Conjecture states that there is a time at which a given runner is at distance at least $1 / (k + 1)$ from all the others. The conjecture has been already settled up to seven ( $k \leq 6$ ) runners while it is open for eight or more runners. In this paper the conjecture has been verified for four or more runners having some particular speeds using elementary tools.

Addendum to: On volumes of arithmetic quotients of SO (1, n)

Mikhail Belolipetsky (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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There are errors in the proof of uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further developments.