On the number of lattice convex chains

Julien Bureaux (MODAL'X); Modal'x); Nathana\"el Enriquez (LPMA

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On the number of lattice convex chains

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arxiv 1603.09587 v2 pith:XWQ4LN7B submitted 2016-03-31 math.PR math.CO

Julien Bureaux (MODAL'X) , Nathanaël Enriquez (LPMA , MODAL'X) This is my paper

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keywords convexformulalatticenumberasymptoticchainsconditiondiagonal

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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.

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