An energy decomposition theorem for matrices and related questions
Mohammadi A, Pham T, Wang Y. 2023. An energy decomposition theorem for matrices and related questions. Canadian Mathematical Bulletin. 66(4), 1280–1295.
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Author
Mohammadi, Ali;
Pham, Thang;
Wang, YitingISTA 
Department
Abstract
Given A⊆GL2(Fq), we prove that there exist disjoint subsets B,C⊆A such that A=B⊔C and their additive and multiplicative energies satisfying max{E+(B),E×(C)}≪|A|3/M(|A|), where
M(|A|)=min{q4/3/|A|1/3(log|A|)2/3,|A|4/5/q13/5(log|A|)27/10}.
We also study some related questions on moderate expanders over matrix rings, namely, for A,B,C⊆GL2(Fq), we have |AB+C|, |(A+B)C|≫q4, whenever |A||B||C|≫q10+1/2. These improve earlier results due to Karabulut, Koh, Pham, Shen, and Vinh ([2019], Expanding phenomena over matrix rings, ForumMath., 31, 951–970).
Publishing Year
Date Published
2023-12-01
Journal Title
Canadian Mathematical Bulletin
Publisher
Cambridge University Press
Volume
66
Issue
4
Page
1280-1295
ISSN
eISSN
IST-REx-ID
Cite this
Mohammadi A, Pham T, Wang Y. An energy decomposition theorem for matrices and related questions. Canadian Mathematical Bulletin. 2023;66(4):1280-1295. doi:10.4153/S000843952300036X
Mohammadi, A., Pham, T., & Wang, Y. (2023). An energy decomposition theorem for matrices and related questions. Canadian Mathematical Bulletin. Cambridge University Press. https://doi.org/10.4153/S000843952300036X
Mohammadi, Ali, Thang Pham, and Yiting Wang. “An Energy Decomposition Theorem for Matrices and Related Questions.” Canadian Mathematical Bulletin. Cambridge University Press, 2023. https://doi.org/10.4153/S000843952300036X.
A. Mohammadi, T. Pham, and Y. Wang, “An energy decomposition theorem for matrices and related questions,” Canadian Mathematical Bulletin, vol. 66, no. 4. Cambridge University Press, pp. 1280–1295, 2023.
Mohammadi A, Pham T, Wang Y. 2023. An energy decomposition theorem for matrices and related questions. Canadian Mathematical Bulletin. 66(4), 1280–1295.
Mohammadi, Ali, et al. “An Energy Decomposition Theorem for Matrices and Related Questions.” Canadian Mathematical Bulletin, vol. 66, no. 4, Cambridge University Press, 2023, pp. 1280–95, doi:10.4153/S000843952300036X.
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