3 papers
math.NT2026
Cubic surfaces failing the integral Hasse principle
Julian Lyczak, Vladimir Mitankin, H. Uppal
We study the integral Brauer--Manin obstruction for affine diagonal cubic surfaces, which we employ to construct the first counterexamples to the integral Hasse principle in this s…
math.NT2025
Counting quadratic points on Fano varieties
Francesca Balestrieri, Kevin Destagnol, Julian Lyczak +2
This paper initiates the systematic study of the number of points of bounded height on symmetric squares of weak Fano varieties. We provide a general framework for establishing the…
math.NT2025
Local solubility in generalised Châtelet varieties
Kevin Destagnol, Julian Lyczak, Efthymios Sofos
We obtain asymptotic formulas for averages of general multivariate arithmetic functions evaluated at polynomial arguments using recent work of Rydin Myerson and Rome-Yamagishi. We…