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Pattern equivariant cohomology and theorems of Kesten and Oren. (English) Zbl 1402.52023
Summary: In 1966, Harry Kesten [Acta Arith. 12, 193–212 (1966; Zbl 0144.28902)] settled the Erdős-Szüsz conjecture on the local discrepancy of irrational rotations. His proof made heavy use of continued fractions and Diophantine analysis. In this paper, we give a purely topological proof of Kesten’s theorem (and I. Oren’s generalization of it [Isr. J. Math. 42, 353–360 (1982; Zbl 0533.28009)]) using the pattern equivariant cohomology of aperiodic tiling spaces.

MSC:
52C23 Quasicrystals and aperiodic tilings in discrete geometry
37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010)
11K38 Irregularities of distribution, discrepancy
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