Sums of four squareful numbers

Abstract

We find an asymptotic formula for the number of primitive vectors $(z_1,\dots ,z_4)\in ({\mathbb{Z}}_{\ne 0}{)}^4$ such that $z_1,\dots ,z_4$ are all squareful and bounded by $B$, and $z_1+\cdots +z_4=0$. Our result agrees in the power of $B$ and $\log B$ with the Campana-Manin conjecture of Pieropan, Smeets, Tanimoto and Várilly-Alvarado.

arXiv comment44 pages

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