Gauss circle problem [SEP] named after
Gauss circle problem
In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and with radius "r". This number is approximated by the area of the circle, so the real problem is to accurately bound the error term describing how the number of points differs from the area.
The first progress on a solution was made by Carl Friedrich Gauss, hence its name.
The problem.
Consider a circle in R with center
To Voronoy and his contemporaries, the formula appeared tailor-made to evaluate certain finite sums. That seemed significant because several important questions in number theory involve finite sums of arithmetic quantities. In this connection, let us mention two classical examples, Dirichlet’s divisor problem and the Gauss’ circle problem. The former estimates the size of "d"("n"),
the number of positive divisors of an integer "n". Dirichlet proved
where formula_2 is Euler’s constant ≈ 0.57721566. Gauss’ circle problem concerns