4 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 HanÄl
We obtain positive lower bounds on the Hausdorff dimension of sets of real numbers given by expressions of the form , where satisfies som…
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…
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…