A diophantine problem concerning cubes

A Diophantine System Concerning Sums of Cubes

We study the Diophantine system

A Diophantine Problem concerning Polygonal Numbers

Motivated by some earlier Diophantine works on triangular numbers by Ljunggren and Cassels, we consider similar problems for general polygonal numbers.

On a Problem of W. J. Leveque concerning Metric Diophantine Approximation

∣ ≤ f(log q) q2 where f is a fixed function satisfying suitable assumptions. Suppose that x is randomly chosen in the unit interval. In a series of papers that appeared in earlier issues of this journal, LeVeque raised the question whether or not the central limit theorem holds for the solution set of the above inequality (compare also with some work of Erdős). Here, we are going to extend and ...

On a Problem of W. J. Leveque concerning Metric Diophantine Approximation Ii

In the first part of this series of papers, we solved LeVeque’s problem that was to establish a central limit theorem for the number of solutions of the diophantine inequality ∣∣∣∣x− pq ∣∣∣∣ ≤ f(log q) q2 in unknowns p, q with q > 0, where f is a function satisfying special assumptions and x is chosen randomly in the unit interval. In this continuation, we are interested in the almost sure beha...

The Diophantine Frobenius Problem