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Let l be a prime number and let k = Fq be a finite field of characteristic p � = l with q = p f elements. Let n ≥ 1. The curve is smooth of genus gn = ϕ(ln+1) Cn: y l = x(x ln − 1) 2 = ln (l−1) 2 over k. Let Fn/k be the function field of Cn, let PFn denote the set of places, and let DivFn denote the group of divisors of Fn/k. The absolute norm N(P) of a place P ∈ PFn is the cardinality of its residue class field. It holds N(P) = q deg P, with a natural number deg P ≥ 1, the degree of P. The Zeta function of the curve Cn is a meromorphic function in the complex plane, defined for Re s> 1 by ζCn(s) = � P∈PF