Let the area of a lattice polygon be s and the sum of the lattice points on each side be x.
A lattice polygon has only one lattice point, and the corresponding relationship between their area and the sum of lattice points on each side is as follows. Please write the relationship between s and X. ..
Lattice origin
The lattice problem originated from the study of the following two problems:
1, Dirichlet divisor problem, that is, to find x >；; D2 (x) at 1 = the number of lattice points on the region {1≤u≤x, 1≤v≤x, uv≤x}. In 1849, Dirichlet proved that D2 (x) = xlnx+(2 v-1) x+△ (x), where v is Euler constant and △(x)=O(x0.5). The purpose of this problem is to find a lower supremum θ0 that makes the remainder estimation △(x)=O(x) hold.
2. For the lattice problem in a circle, let x >；; 1, A2(x)= the number of lattice points on μ+ν≤x in a circle. Gauss proved that A2(x)=πx+R(x), where R(x)=O(x 1/2), and the problem of finding the lower supremum α of λ of the co-estimation R(x)=O(x) is called the problem of lattice points in a circle or Gauss circle.