A congruence sum and rational approximations
Number Theory
2017-01-25 v1
Abstract
We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula is a simple consequence of this fact.
Cite
@article{arxiv.1701.06614,
title = {A congruence sum and rational approximations},
author = {Sandro Bettin},
journal= {arXiv preprint arXiv:1701.06614},
year = {2017}
}
Comments
7 pages, 2 figures, to appear in Rend. Circ. Mat. Palermo, II. Ser