Published January 11, 2020
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Higher Distance Energies and Expanders with Structure
- Creators
- Pohoata, Cosmin
- Sheffer, Adam
Abstract
We adapt the idea of higher moment energies, originally used in Additive Combinatorics, so that it would apply to problems in Discrete Geometry. This new approach leads to a variety of new results, such as (i) Improved bounds for the problem of distinct distances with local properties. (ii) Improved bounds for problems involving expanding polynomials in R[x,y] (Elekes-Ronyai type bounds) when one or two of the sets have structure. Higher moment energies seem to be related to additional problems in Discrete Geometry, to lead to new elegant theory, and to raise new questions.
Additional Information
Supported by NSF grant DMS-1710305.Attached Files
Submitted - 1709.06696.pdf
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1709.06696.pdf
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Additional details
- Eprint ID
- 100649
- Resolver ID
- CaltechAUTHORS:20200110-160143789
- DMS-1710305
- NSF
- Created
-
2020-01-11Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field