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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 14. Issue 1


Published on

June, 2019


Pages

1-10


DOI

https://doi.org/10.2478/udt-2019-0001

Article

Higher Order Oscillation and Uniform Distribution


Authors

Shigeki Akiyama and Yunping Jiang


Abstract

It 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∈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 polynomials Q(x), sequences (αβng(β)+ Q(n)) n∈ℕ are uniformly distributed modulo 1.


Citation

Akiyama, S. & Jiang, Y. (2019). Higher Order Oscillation and Uniform Distribution. Uniform distribution theory, 14(1), 1-10. https://doi.org/10.2478/udt-2019-0001