Date:
Thu, 09/01/202512:15-14:00
Location:
Ross 70
Title: The number variance of dilations of integer sequences. Nadav Yesha
Abstract: Let (x_n) be a sequence of positive integers. We will discuss the fluctuation of the number of elements modulo 1 of dilations (\alpha x_n) in short intervals, for generic values of alpha. The main motivation is to compare statistics such as the number variance with the random model, thereby observing pseudo-random behaviour for some interesting examples, such as x_n = n^2. Based on joint works with Zonglin Li and with Christoph Aistleitner (in progress).
Abstract: Let (x_n) be a sequence of positive integers. We will discuss the fluctuation of the number of elements modulo 1 of dilations (\alpha x_n) in short intervals, for generic values of alpha. The main motivation is to compare statistics such as the number variance with the random model, thereby observing pseudo-random behaviour for some interesting examples, such as x_n = n^2. Based on joint works with Zonglin Li and with Christoph Aistleitner (in progress).