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Number Theory Seminar

Pair correlation of monomial sequences modulo 1

Chris Lutsko (Rutgers)

Location:  zoom
Date & time: Tuesday, 21 September 2021 at 2:30PM - 3:30PM

Abstract: Fix \(alpha, theta > 0\), and consider the sequence \((alpha n^theta mod 1)_{n>0}\). Since the seminal work of Rudnick-Sarnak (1998), and due to the Berry-Tabor conjecture in quantum chaos, the fine-scale properties of these dilated mononomial sequences have been intensively studied. In this talk, I will present a recent result (joint with Sourmelidis and Technau) showing that for \(theta le 1/3\), and \(alpha > 0\), the pair correlation function is Poissonian. Moreover, I will discuss ongoing work to extend this result to higher correlations.

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