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On the higher-order Titchmarsh divisor problem
Abstract
For every fixed integer k≥2 and every fixed nonzero integer h, we prove that, as x→∞, ∑x<n≤2xΛ(n)τk(n+h) ∼ Ck,hx(log x)k−1, where τk is the k-fold divisor function and Ck,h>0 is a constant depending only on k and h.
Related
BibTeX
@misc{hu2026higherorder,
title = {{On the higher-order Titchmarsh divisor problem}},
author = {Guangwei Hu and Guangshi Lü and Zhiwei Wang and Jie Wu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.12756},
eprint = {2611.12756},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.12756},
}
RIS
TY - UNPB
TI - On the higher-order Titchmarsh divisor problem
AU - Guangwei Hu
AU - Guangshi Lü
AU - Zhiwei Wang
AU - Jie Wu
PY - 2026
DA - 2026/11/09
PB - arXiv
DO - 10.48550/arxiv.2611.12756
UR - https://arxiv.org/abs/2611.12756
AB - For every fixed integer k≥2 and every fixed nonzero integer h, we prove that, as x→∞, ∑_x<n≤2xΛ(n)τ_k(n+h) ∼ C_k,hx(log x)^k−1, where τ_k is the k-fold divisor function and C_k,h>0 is a constant depending only on k and h.
ER -