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Date
2021-09Type
- Journal Article
ETH Bibliography
yes
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Abstract
For E ⊂ Fqd, let Δ(E) denote the distance set determined by pairs of points in E. By using additive energies of sets on a paraboloid, Koh, Pham, Shen, and Vinh (2020) proved that if E, F ⊂ Fqdare subsets with |E|·|F| >> qd+1/3, then |Δ(E) + Δ(F)|>q/2. They also proved that the threshold qd+1/3 is sharp when |E|=|F|. In this paper, we provide an improvement of this result in the unbalanced case, which is essentially sharp in odd dimensions. The most important tool in our proofs is an optimal L2 restriction theorem for the sphere of zero radius. Show more
Publication status
publishedExternal links
Journal / series
Proceedings of the Steklov Institute of MathematicsVolume
Pages / Article No.
Publisher
InterperiodicaOrganisational unit
03457 - Welzl, Emo / Welzl, Emo
Funding
191067 - Erdos-Falconer Distance Conjecture and Related Topics (SNF)
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ETH Bibliography
yes
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