Questions on rational approximations to a real number can be generalized in two directions. On the one hand, we may ask about "approximation" to a point in ℝⁿ by hyperplanes defined over the rationals ...

Let C be a nondegenerate planar curve and for a real, positive decreasing function ψ let C(ψ) denote the set of simultaneously ψ-approximable points lying on C. We show that C is of Khintchine type ...

Arithmetic geometry and Diophantine geometry lie at the confluence of number theory and algebraic geometry, exploring the deep connections between the arithmetic properties of numbers and the ...

The University of Colorado Center for Number Theory has interests spanning number theory, from analytic to algebraic. There is a focus on arithmetic geometry, including arithmetic dynamics, elliptic ...