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SUM-PRODUCT ESTIMATES VIA DIRECTED EXPANDERS
- Publisher
- de Gruyter
- Copyright
- © 2019 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/forum-2019-0032
- Publisher site
- See Article on Publisher Site
Abstract
AbstractIn this paper, we study expanding phenomena in the setting of matrix rings.More precisely, we will prove that•if A is a set of M2(𝔽q){M_{2}(\mathbb{F}_{q})}and |A|≫q7/2{\lvert A\rvert\gg q^{7/2}}, then|A(A+A)|,|A+AA|≫q4{\lvert A(A+A)\rvert,\lvert A+AA\rvert\gg q^{4}},•if A is a set of SL2(𝔽q){\mathrm{SL}_{2}(\mathbb{F}_{q})}and |A|≫q5/2{\lvert A\rvert\gg q^{5/2}}, then|A(A+A)|,|A+AA|≫q4{\lvert A(A+A)\rvert,\lvert A+AA\rvert\gg q^{4}}.We also obtain similar results for the cases of A(B+C){A(B+C)}and A+BC{A+BC}, where A,B,C{A,B,C}are sets in M2(𝔽q){M_{2}(\mathbb{F}_{q})}.
Journal
Forum Mathematicum – de Gruyter
Published: Jul 1, 2019