Newton Polygons of L-functions Associated to Deligne Polynomials

A conjecture of Le says that the Deligne polytope $Δ_d$ is generically ordinary if $p\equiv 1\ (\!\!\bmod\ D(Δ_d))$, where $D(Δ_d)$ is a combinatorial constant determined by $Δ_d$. In this paper a counterexample is given to show that the conjecture is not true in general.

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