Higher Order Oscillation and Uniform Distribution

Shigeki Akiyama, Yunping Jiang
2019 Uniform Distribution Theory  
AbstractIt is known that the Möbius function in number theory is higher order oscillating. In this paper we show that there is another kind of higher order oscillating sequences in the form (e2πiαβn g(β))n∈𝕅, for a non-decreasing twice differentiable function g with a mild condition. This follows the result we prove in this paper that for a fixed non-zero real number α and almost all real numbers β> 1 (alternatively, for a fixed real number β> 1 and almost all real numbers α) and for all real
more » ... lynomials Q(x), sequences (αβng(β)+ Q(n)) n∈𝕅 are uniformly distributed modulo 1.
doi:10.2478/udt-2019-0001 fatcat:b7ksbrl74vbotiu3eb7rxyx4dq