On the number of lattice convex chains

Abstract

An asymptotic formula is presented for the number of planar lattice convex polygonal lines joining the origin to a distant point of the diagonal. The formula involves the non-trivial zeros of the zeta function and leads to a necessary and sufficient condition for the Riemann Hypothesis to hold.

15 pages, 2 figures

Cited by in corpus (1)

• Convex lattice polygonal lines with a constrained number of vertices