Samantha Fairchild

Analogs of the primitive Gauss circle problem

Let N(R) be the number of integer lattice points in the plane of length less than R. The expected value of N(R) is roughly the area of the ball of radius R, V(R). The Gauss circle problem is centered around the question of understanding the discrepancy, D(R) = |N(R)-V(R)|, which is the difference between the actual number of points and the expected number of points. A similar story can be told in the case of the primitive Gauss circle problem where instead of counting all integer lattice points, we restrict to lattice points whose entries are coprime. We will share expected value and discrepancy type results for counting discrete subsets which generalize the primitive integer lattice points.