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

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

2011-10-31

arxiv.org/abs/1110.6864v1

Mathematics

Number Theory

Scientific paper

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.

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