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arXiv · 2111.07882

Functional Equations Associated to Collatz-Type Maps on Integer Rings of Algebraic Number Fields

M. C. Siegel
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Abstract

In 1995, Meinardus & Berg presented a reformulation of the Collatz Conjecture in terms of a functional equation in a single complex variable over the open unit disk. This paper generalizes that method to deal with not only a large class of Collatz-type maps defined on the integers, but further generalizations thereof to Collatz-type maps on the rings of integers on an arbitrary algebraic number field.

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M. C. Siegel. 2021-11-10. Functional Equations Associated to Collatz-Type Maps on Integer Rings of Algebraic Number Fields. https://arxiv.org/abs/2111.07882

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