R. Vaughan

activity

20112018

most citedDiophantine approximation on manifolds and lower bounds for Hausdorff dimension

7 citations · 9 across the 2 of their papers we have counts for

collaborators

3 papers

math.NT2018

Diophantine approximation on curves and the distribution of rational points: divergence theory

V. Beresnevich, R. C. Vaughan, S. Velani +1

In this paper we develop a new explicit method to studying rational points near manifolds and obtain optimal lower bounds on the number of rational points of bounded height lying a…

math.NT2017★ 7 cited

Diophantine approximation on manifolds and lower bounds for Hausdorff dimension

Victor Beresnevich, Lawrence Lee, Robert C. Vaughan +1

Given $n \in N$ and $τ > \frac{1}{n}$ , let $S_{n} (τ)$ denote the classical set of $τ$ -approximable points in $R^{n}$ , which consists of $x \in R^{n}$ th…

math.NT2011★ 2 cited

Mean Value Theorems for Binary Egyptian Fractions

Jing-Jing Huang, Robert C. Vaughan

In this paper, we establish two mean value theorems for the number of solutions of the Diophantine equation $\frac{a}{n} = \frac{1}{x} + \frac{1}{y}$ , in the case when $a$ is fixed and…