arXiv Analytics

Sign in

arXiv:1110.6864 [math.NT]AbstractReferencesReviewsResources

Asymptotics for numbers of line segments and lines in a square grid

Pentti Haukkanen, Jorma K. Merikoski

Published 2011-10-31Version 1

We present an asymptotic formula for the number of line segments connecting q+1 points of an nxn square grid, and a sharper formula, assuming the Riemann hypothesis. We also present asymptotic formulas for the number of lines through at least q points and, respectively, through exactly q points of the grid. The well-known case q=2 is so generalized.

Journal: International Journal of Number Theory 2012
Categories: math.NT, cs.IT, math.CO, math.IT
Subjects: 05A99, 11N37, 11P21
Related articles: Most relevant | Search more
arXiv:1401.1514 [math.NT] (Published 2014-01-07)
An Elementary Proof of an Asymptotic Formula of Ramanujan
arXiv:1203.6473 [math.NT] (Published 2012-03-29, updated 2012-11-10)
A note on the number of abelian groups of a given order
arXiv:math/0507259 [math.NT] (Published 2005-07-13)
Asymptotic formula for sum-free sets in abelian groups

Links

Toolbox