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Creators/Authors contains: "Shubin, Andrei"

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  1. ; (, International Mathematics Research Notices)
    Abstract We show that sequences of the form $$\alpha n^{\theta } \pmod {1}$$ with $$\alpha> 0$$ and $$0 < \theta < \tfrac {43}{117} = \tfrac {1}{3} + 0.0341 \ldots $$ have Poissonian pair correlation. This improves upon the previous result by Lutsko, Sourmelidis, and Technau, where this was established for $$\alpha> 0$$ and $$0 < \theta < \tfrac {14}{41} = \tfrac {1}{3} + 0.0081 \ldots $$. We reduce the problem of establishing Poissonian pair correlation to a counting problem using a form of amplification and the Bombieri–Iwaniec double large sieve. The counting problem is then resolved non-optimally by appealing to the bounds of Robert–Sargos and (Fouvry–Iwaniec–)Cao–Zhai. The exponent $$\theta = \tfrac {2}{5}$$ is the limit of our approach. 
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