@article{Wang2023, 
author = {Huimin Wang and Liqun Hu},
title = {Sums of the higher divisor function of diagonal homogeneous forms in short intervals},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {22577-22592},
keywords = {circle method, divisor problem, short intervals},
url = {https://www.sciopen.com/article/10.3934/math.20231150},
doi = {10.3934/math.20231150},
abstract = {Let        d    k    (  n  ) denote the k-th divisor function. In this paper, we give the asymptotic formula of the sum         ∑                                                      x              −              y              ≤                              n                i                r                            ≤              x              +              y                                                          i              =              1              ,              2              ,              …              ,              l                                                      d      k        (          n      1      r        +          n      2      r        +    …    +          n      l      r        )    ,where        n    1    ,      n    2    ,  …  ,      n    l    ∈            Z        +  ,    k  ≥  2,    r  ≥  3 and    l  >      2          r      −      1       are integers.}
}