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On the number of lattice convex chains
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On the number of lattice convex chains
classification
math.PR
math.CO
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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