Sums of four squareful numbers

Alec Shute

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arXiv · 2104.06966

Sums of four squareful numbers

Alec Shute

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Abstract

We find an asymptotic formula for the number of primitive vectors $(z_1,\ldots,z_4)\in (\mathbb{Z}_{\neq 0})^4$ such that $z_1,\ldots, z_4$ 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 V\'{a}rilly-Alvarado.

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Alec Shute. 2021-04-14. Sums of four squareful numbers. https://arxiv.org/abs/2104.06966

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