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The article provides a sufficient condition for a locally finite module overthe absolute Galois group of a finite field F to satisfy the Riemann HypothesisAnalogue with respect to the projective line. The condition holds for allsmooth irreducible projective curves of positive genus, defined over F. Byconstruction of an explicit example we establish that the scope of our mainresult is larger than the class of the smooth irreducible projective varieties,defined over F.

Riemann Hypothesis Analogue for locally finite modules over the absolute Galois group of a finite field