A three gap theorem for the adeles

Akshat Das; Alan Haynes

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arXiv · 2107.05147

A three gap theorem for the adeles

Akshat Das·Alan Haynes

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Abstract

We prove a natural generalization of the classical three gap theorem, for rotations on adelic tori. Our proof is an adaptation to the adeles of the lattice based approach to gaps problems in Diophantine approximation originally introduced by Marklof and Str\"ombergsson.

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Akshat Das, Alan Haynes. 2021-07-11. A three gap theorem for the adeles. https://arxiv.org/abs/2107.05147

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