The k-fold divisor function over the intersection of Piatetski-Shapiro sequences

¹ School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, China
² School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, Jiangsu, China

^* Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 18 December 2025
Accepted: 9 February 2026

Abstract

The average of the fc-fold divisor function

d_k(n) = ≠{ (a₁,…a_k) ∈ ℤ_>0^k:a₁⋯a_k = n }

has been widely studied. The Piatetski-Shapiro sequences are of the form N^c = (⌊ n^c ⌋)_n=1^∞ with c > 1, c ∉ ℕ. In this article, we estimate the average of the k-fold divisor function over the intersection of Piatetski-Shapiro sequences.