For generic f of degree d not divisible by p, the a-number of the Artin-Schreier curve y^p - y = f(x) equals the Booher-Cais lower bound, making that bound sharp.
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Minimal $a$-numbers of Artin--Schreier covers of ordinary curves
For generic f of degree d not divisible by p, the a-number of the Artin-Schreier curve y^p - y = f(x) equals the Booher-Cais lower bound, making that bound sharp.