# Seminars & Colloquia Calendar

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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