A Note on Lower Bounds for Frobenius Traces
نویسندگان
چکیده
Without the hypothesis “ordinary” the answer can be no, because for a supersingular elliptic curve one can have A(n) = 0 on entire arithmetic progressions of n. On the other hand, all the A(n) in the supersingular case are divisible, as algebraic integers, by qn/2, so the nonzero A(n) must have |A(n)| ≥ qn/2. If instead E/Fq is ordinary, then all the A(n) are nonzero because they are all prime to p, so this vanishing problem at least disappears.
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