@article{Li2025, 
author = {Ruiyang Li and Hai Yang},
title = {Asymptotic formulas for Dirichlet convolutions},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {19540-19553},
keywords = {prime-number-theorem, Piltz divisor function, asymptotic formula, Dirichlet convolution, Riemann zeta-function},
url = {https://www.sciopen.com/article/10.3934/math.2025872},
doi = {10.3934/math.2025872},
abstract = {In this paper, we use convoluting prime-number-theorem-related functions (Mobius, von Mangoldt, and Liouville) by the Piltz divisor function to research an asymptotic formula for the convolution sum    (  x  ≥  1  ). Our main result is Theorem 1, which separates the error terms for the PNT-related functions and the Piltz divisor function. Under the assumption of the conjectural estimate for the latter, we obtain the expected error term as in PNT.}
}