Some new results on higher energies
Abstract
In the paper we develop the method of higher energies. New upper bounds for the additive energies of convex sets, sets A with small |AA| and |A(A+1)| are obtained. We prove new structural results, including higher sumsets, and develop the notion of dual popular difference sets.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2012
- DOI:
- 10.48550/arXiv.1212.6414
- arXiv:
- arXiv:1212.6414
- Bibcode:
- 2012arXiv1212.6414S
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 38 pages