PreprintCC BY-SA 4.0arXiv
Two-point correlations of multiplicative functions with dense orbits
Abstract
Let f,g:ββπ be completely multiplicative functions with dense images in the complex unit circle π. We prove that, for every non-empty open set U β π2, the set of integers n such that (f(n),g(n+1)) β U has positive upper logarithmic density, unless the pair (f,g) is of a special form. This result strengthens earlier theorems of Klurman and Mangerel, as well as of Charamaras, Mountakis, and Tsinas, and yields simpler proofs.
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BibTeX
@misc{tardy2026twopoint,
title = {{Two-point correlations of multiplicative functions with dense orbits}},
author = {NΓ©o Tardy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.26814},
eprint = {2608.26814},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26814},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Two-point correlations of multiplicative functions with dense orbits
AU - NΓ©o Tardy
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2608.26814
UR - https://arxiv.org/abs/2608.26814
AB - Let f,g:ββπ be completely multiplicative functions with dense images in the complex unit circle π. We prove that, for every non-empty open set U β π^2, the set of integers n such that (f(n),g(n+1)) β U has positive upper logarithmic density, unless the pair (f,g) is of a special form. This result strengthens earlier theorems of Klurman and Mangerel, as well as of Charamaras, Mountakis, and Tsinas, and yields simpler proofs.
ER -