Abstract
In this paper we consider the curves Ck(p,a):yp−y=xpk+1+ax defined over Fp and give a positive answer to a conjecture about a divisibility condition on L-polynomials of the curves Ck(p,a). Our proof involves finding an exact formula for the number of Fpn-rational points on Ck(p,a) for all n, and uses a result we proved elsewhere about the number of rational points on supersingular curves.
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