On Erdos-Falconer distance problem in even dimensions

2026/07/19 by Thang Pham, Chun-Yen Shen, Boqing Xue
#math.NT #math.CA #math.CO

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Abstract

Let q be an odd prime power and \mathbbF_q be the finite field of order q. We prove an extraction theorem for the Erdős-Falconer distance conjecture in even dimensions, showing that the conjecture for all even dimensions reduces to the planar case. As consequences, we obtain improved thresholds on the pinned distance problem and the distribution of triangles, achieving new records of (d)/(2)+(1)/(4) over prime fields and (d+1)/(2)+(1)/(10) over arbitrary finite fields, respectively.

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