6 papers
Quantitative Khintchine on the parabola with non-monotonic approximation functions
Maiken Gravgaard, Simon Kristensen
We prove a quantitative version of the convergence case of Khintchine's celebrated theorem in metric Diophantine approximation, but where the approximated points are restricted to…
Lower bounds for the Hausdorff dimension of expressible sets
Maiken Gravgaard, Simon Kristensen, Jaroslav Hančl
We obtain positive lower bounds on the Hausdorff dimension of sets of real numbers given by expressions of the form , where satisfies som…
Algebraic independence of infinite series
Jaroslav Hancl, Mathias L. Laursen, Simon Kristensen
We give conditions on a finite set of series of rational numbers to ensure that they are algebraically independent. Specialising our results to polynomials of lower degree, we also…
Asymptotics for partitions over the Fibonacci numbers and related sequences
Michael Coons, Simon Kristensen, Mathias L. Laursen
In this paper, harkening back to ideas of Hardy and Ramanujan, Mahler and de Bruijn, with the addition of more recent results on the Fibonacci Dirichlet series, we determine the as…
On the distribution of sequences of the form
S. Kristensen, T. Persson
We study the distribution of sequences of the form , where is some increasing sequence of integers. In particular, we study the Lebesgue m…
Khintchine's theorem and transference principle for star bodies
M. M. Dodson, S. Kristensen
Analogues of Khintchine's Theorem in simultaneous Diophantine approximation in the plane are proved with the classical height replaced by fairly general planar distance functions o…