Alec Shute

activity

20212025

most citedSums of four squareful numbers

2 citations · 2 across the 3 of their papers we have counts for

collaborators

3 papers

math.NT2025

Local solubility of generalised Fermat equations

Peter Koymans, Ross Paterson, Tim Santens +1

For every $n \geq 2$ we determine the asymptotic formula for the number of integer triples $(a, b, c)$ of bounded absolute value such that the generalised Fermat equation given by $a…

math.NT2024

Semi-integral points of bounded height on toric varieties

Alec Shute, Sam Streeter

We prove asymptotics for semi-integral points of bounded height on toric varieties. We verify the Manin-type conjecture of Pieropan, Smeets, Tanimoto and Várilly-Alvarado for smoot…

math.NT2021★ 2 cited

Sums of four squareful numbers

Alec Shute

We find an asymptotic formula for the number of primitive vectors $(z_{1}, \dots, z_{4}) \in (Z_{\neq = 0})^{4}$ such that $z_{1}, \dots, z_{4}$ are all squareful and bounded by $B$ , an…