The distribution of spacings of real-valued lacunary sequences modulo one

Chaubey, Sneha; Yesha, Nadav

doi:10.48550/arxiv.2108.00431

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2021

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Cited by 1 publication

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References 11 publications

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“…An exception is the work of Yesha and the second named author [TY20], who showed that (n α mod 1)n has Poissonian m-point correlation, for almost all α > 4m 2 − 4m−1. Moreover, for lacunary sequences we refer to Rudnick and Zaharescu [RZ99, RZ02], for dilations of lacunary integer sequences; and Chaubey and Yesha [CY21] where this is extended to dilations of real-valued sequences.…”

Section: Historymentioning

confidence: 99%

Correlations of the Fractional Parts of $αn^θ$

Lutsko¹,

Technau²

2021

Preprint

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Let m ≥ 3, we prove that (αn θ mod 1)n>0 has Poissonian m-point correlation for all α > 0, provided θ < θm, where θm is an explicit bound which goes to 0 as m increases. This work builds on the method developed in Lutsko-Sourmelidis-Technau (2021), and introduces a new combinatorial argument for higher correlation levels, and new Fourier analytic techniques. A key point is to introduce an 'extra' frequency variable to de-correlate the sequence variables and to eventually exploit a repulsion principle for oscillatory integrals. Presently, this is the only positive result showing that the m-point correlation is Poissonian for such sequences.

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Section: Historymentioning

confidence: 99%