Integer points in a simplex and related Diophantine problems: Hardy--Littlewood asymptotics in higher dimensions

TL;DR

This paper extends Hardy and Littlewood's 1920s results on counting integer points in irrationally inclined triangles to higher-dimensional simplices, providing asymptotic formulas in multiple dimensions.

Contribution

It generalizes Hardy-Littlewood asymptotics for integer points in triangles to higher-dimensional simplices, advancing Diophantine approximation theory.

Findings

Derived asymptotic formulas for integer points in higher-dimensional simplices.

Extended classical 2D results to n-dimensional cases.

Contributed to understanding Diophantine problems in higher dimensions.

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.