On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method
Abstract
The Falconer distance problem for Cartesian product sets was introduced and studied by Iosevich and Liu (MR3525385). In this paper, by implementing a new observation on Cartesian product sets associated with a particular parabolic structure, we study the pinned version of Falconer distance problem for Cartesian product sets, and improve the threshold for the Falconer distance set in MR3525385 in certain case.
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