We fix a monic polynomial $/bar f(x) /in /FF_q[x]$ over a finite field of characteristic $p$, and consider the $/ZZ_{p^{l}}$-Artin--Schreier--Witt tower defined by $/bar f(x)$; this is a tower of curves $/cdots /to C_m /to C_{m-1} /to /cdots /to C_0 =/mathbb{A}^1$, whose Galois group is canonically isomorphic to $/ZZ_{p^l}$, the degree $l$ unramified extension of $/ZZ_p$, which is abstractly isomorphic to $(/ZZ_p)^l$ as a topological group.
We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function
asymptotically form a finite union of arithmetic progressions. As a corollary, we prove the spectral halo property of the spectral variety associated to the $/ZZ_{p^{l}}$-Artin--Schreier--Witt tower. This extends the main result in [DWX] from rank one case $l=1$ to the higher rank case $l/geq 1$.

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