Integer points in a simplex and related Diophantine problems: Hardy--Littlewood asymptotics in higher dimensions
arXiv:2605.14446
summary
The paper generalizes Hardy and Littlewood’s 1920s results on counting integer points in right‑angled triangles with irrational slopes to counting integer points in higher‑dimensional simplices, providing asymptotic formulas.
Abstract
In the early 1920s, Hardy and Littlewood considered the number of integer points in the right-angled triangles with irrational inclines of the diagonal. We extend their results to higher dimensions.
Topics & keywords
#integer lattice points#simplex#diophantine problems#hardy–littlewood method#asymptotic enumeration#higher dimensionsinteger pointssimplexHardy–Littlewood asymptoticsDiophantine approximationlattice point countinghigher-dimensional geometry