On diophantine properties of generalized number systems - finite and periodic representations

Abstract: In this talk we investigate elements with special patterns in their representations in number systems in algebraic number fields. We concentrate on periodicity and on the representation of rational integers. We prove under natural assumptions that there are only finitely many $S$-units whose representation is periodic with a fixed period. We prove that the same holds for the set of values of polynomials at rational integers.

dynamical systemsnumber theory

Audience: researchers in the topic

( slides )

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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