An Asymmetric Bound for Sum of Distance Sets Article Swipe

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Daewoong Cheong , Doowon Koh , Thang Pham ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.1134/s0081543821040131

For $ E\subset \mathbb{F}_q^d$, 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\subset \mathbb{F}_q^d $ are subsets with $|E||F|\gg q^{d+\frac{1}{3}}$ then $|Δ(E)+Δ(F)|> q/2$. They also proved that the threshold $q^{d+\frac{1}{3}}$ 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 $L^2$ restriction theorem for the sphere of zero radius.

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Paraboloid Combinatorics Mathematics RADIUS Discrete mathematics Physics Geometry Surface (topology) Computer science Computer security

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Type: preprint
Language: en
Landing Page: https://doi.org/10.1134/s0081543821040131
OA Status: green
References: 19
Related Works: 20
OpenAlex ID: https://openalex.org/W3053780662

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DOI: https://doi.org/10.1134/s0081543821040131

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Title: An Asymmetric Bound for Sum of Distance Sets

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Language: en

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Publication year: 2021

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Publication date: 2021-09-01

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Authors: Daewoong Cheong, Doowon Koh, Thang Pham

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Landing page: https://doi.org/10.1134/s0081543821040131

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Concepts: Paraboloid, Combinatorics, Mathematics, RADIUS, Discrete mathematics, Physics, Geometry, Surface (topology), Computer science, Computer security

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abstract_inverted_index.q^{d+\frac{1}{3}}$	42
abstract_inverted_index.$q^{d+\frac{1}{3}}$	52
cited_by_percentile_year
countries_distinct_count	3
institutions_distinct_count	3
citation_normalized_percentile.value	0.08603989
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False