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.

44 pages

References in corpus (1)

• Birational geometry for number theorists