Improved Averaged Distribution of $d_3(n)$ in Prime Arithmetic Progressions

Metin Can Aydemir, Muhammet Boran

We say that $d_3(n)$ has exponent of distribution $\theta$ if, for every $\epsilon >0$, the expected asymptotic holds uniformly for all moduli $q\le x^{\theta -\epsilon }$. Nguyen proved…