On the number of lattice convex chains

TL;DR

This paper derives an asymptotic formula for counting lattice convex chains, linking it to the zeros of the zeta function and providing a criterion related to the Riemann Hypothesis.

Contribution

It introduces a new asymptotic formula for lattice convex chains that involves the zeros of the zeta function, connecting combinatorics with number theory.

Findings

Asymptotic formula involving zeta zeros

Necessary and sufficient condition for Riemann Hypothesis

Bridges combinatorics and number theory

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.