For A in F_q^2 with |A| at most p^{4/3}, some point of A determines Ω(|A|^{2/3}) distinct distances, improving the earlier Ω(|A|^{20/37}) bound.
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Bisector energy and pinned distances in positive characteristic
For A in F_q^2 with |A| at most p^{4/3}, some point of A determines Ω(|A|^{2/3}) distinct distances, improving the earlier Ω(|A|^{20/37}) bound.