On Unit Fractions with Denominators in Short Intervals
Number Theory
2007-05-23 v1
Abstract
We answer several questions of P. Erdos and R. Graham by showing that for any rational number r > 0, there exist integers n1, n2, ..., nk, k variable, where N < n1 < n2 < ... < nk < (e^r + o_r(1) ) N, such that r = 1/n1 + 1/n2 + ... + 1/nk. Moreover, we obtain the best-possible error term for the o_r(1), which is O_r(loglog N/log N).
Cite
@article{arxiv.math/9904181,
title = {On Unit Fractions with Denominators in Short Intervals},
author = {Ernest S. Croot},
journal= {arXiv preprint arXiv:math/9904181},
year = {2007}
}
Comments
19 pages amstex, no figures