# Integral point

2010 Mathematics Subject Classification: Primary: 52C07 Secondary: 11H06 [MSN][ZBL]

A point in an $n$-dimensional space $\mathbf R^n$ with integer coordinates. In number theory one studies the problem of the number of integral points in certain domains; for example, for $n=2$ in a disc and for $n=3$ in a ball (see Circle problem), and also the problem of conditions for uniform distribution of integral points on surfaces; for example, for $n=3$ on a sphere or on an ellipsoid. The strongest results are obtained by the method of trigonometric sums and by methods of algebraic and geometric number theory.

Integral points are also called lattice points, since the set $\mathbf Z^n\subset\mathbf R^n$ is an example of a lattice of points.