Expansion for the product of matrices in groups
-
Doowon Koh
,
Chun-Yen Shen
Abstract
In this paper, we give strong lower bounds on the size of the sets of products of matrices in some certain groups. More precisely, we prove an analogue of a result due to Chapman and Iosevich for matrices in
Funding source: National Research Foundation of Korea
Award Identifier / Grant number: NRF-2015R1A1A1A05001374
Award Identifier / Grant number: P2ELP2175050
Funding source: Ministry of Science and Technology, Taiwan
Award Identifier / Grant number: 104-2628-M-002-015-MY4
Funding statement: D. Koh was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2015R1A1A1A05001374). T. Pham was supported by Swiss National Science Foundation grant P2ELP2175050. C.-Y. Shen was supported in part by MOST, through grant 104-2628-M-002-015-MY4.
Acknowledgements
The authors would like to deeply thank Oliver Roche-Newton and Ilya Shkredov for many helpful discussions that make nice improvement for our Theorem 1.3. The authors would like to thank the referee for valuable suggestions.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
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- Expansion for the product of matrices in groups
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Articles in the same Issue
- Frontmatter
- Sharp maximal estimates for multilinear commutators of multilinear strongly singular Calderón–Zygmund operators and applications
- Infinite-dimensional triangularizable algebras
- Expansion for the product of matrices in groups
- Asphericity of positive free product length 4 relative group presentations
- Unitary representations with non-zero Dirac cohomology for complex E6
- On middle cohomology of special Artin–Schreier varieties and finite Heisenberg groups
- Normal elements of noncommutative Iwasawa algebras over SL3(ℤ_p)
- Regularity properties of Schrödinger equations in vector-valued spaces and applications
- Statistics of Hecke eigenvalues for GL(𝑛)
- Bilinear Calderón–Zygmund operators on products of variable Hardy spaces
- On the Reidemeister spectrum of an Abelian group
- Dense free subgroups of automorphism groups of homogeneous partially ordered sets
- Left semi-braces and solutions of the Yang–Baxter equation
- On the automorphism group of a symplectic half-flat 6-manifold
