2 citations · 2 across the 6 of their papers we have counts for
6 papers
Local solubility of generalised Fermat equations
Peter Koymans, Ross Paterson, Tim Santens +1
For every we determine the asymptotic formula for the number of integer triples of bounded absolute value such that the generalised Fermat equation given by $a…
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…
Polynomials represented by norm forms via the beta sieve
Alec Shute
A central question in Arithmetic geometry is to determine for which polynomials and which number fields the Hasse principle holds for the affine equation…
The Bertini irreducibility theorem for higher codimensional slices
Philip Kmentt, Alec Shute
Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their…
Sums of four squareful numbers
Alec Shute
We find an asymptotic formula for the number of primitive vectors such that are all squareful and bounded by , an…
On the leading constant in the Manin-type conjecture for Campana points
Alec Shute
We compare the Manin-type conjecture for Campana points recently formulated by Pieropan, Smeets, Tanimoto and Várilly-Alvarado with an alternative prediction of Browning and Van Va…