Alec Shute

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 VÃ¡rilly-Alvarado for smoo…

math.NT2024

Polynomials represented by norm forms via the beta sieve

Alec Shute

A central question in Arithmetic geometry is to determine for which polynomials $f \in Z [t]$ and which number fields $K$ the Hasse principle holds for the affine equation…