{"_id":"13128","language":[{"iso":"eng"}],"article_type":"original","citation":{"mla":"Mohammadi, Ali, et al. “An Energy Decomposition Theorem for Matrices and Related Questions.” <i>Canadian Mathematical Bulletin</i>, vol. 66, no. 4, Cambridge University Press, 2023, pp. 1280–95, doi:<a href=\"https://doi.org/10.4153/S000843952300036X\">10.4153/S000843952300036X</a>.","ieee":"A. Mohammadi, T. Pham, and Y. Wang, “An energy decomposition theorem for matrices and related questions,” <i>Canadian Mathematical Bulletin</i>, vol. 66, no. 4. Cambridge University Press, pp. 1280–1295, 2023.","ama":"Mohammadi A, Pham T, Wang Y. An energy decomposition theorem for matrices and related questions. <i>Canadian Mathematical Bulletin</i>. 2023;66(4):1280-1295. doi:<a href=\"https://doi.org/10.4153/S000843952300036X\">10.4153/S000843952300036X</a>","chicago":"Mohammadi, Ali, Thang Pham, and Yiting Wang. “An Energy Decomposition Theorem for Matrices and Related Questions.” <i>Canadian Mathematical Bulletin</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.4153/S000843952300036X\">https://doi.org/10.4153/S000843952300036X</a>.","ista":"Mohammadi A, Pham T, Wang Y. 2023. An energy decomposition theorem for matrices and related questions. Canadian Mathematical Bulletin. 66(4), 1280–1295.","apa":"Mohammadi, A., Pham, T., &#38; Wang, Y. (2023). An energy decomposition theorem for matrices and related questions. <i>Canadian Mathematical Bulletin</i>. Cambridge University Press. <a href=\"https://doi.org/10.4153/S000843952300036X\">https://doi.org/10.4153/S000843952300036X</a>","short":"A. Mohammadi, T. Pham, Y. Wang, Canadian Mathematical Bulletin 66 (2023) 1280–1295."},"publication_identifier":{"issn":["0008-4395"],"eissn":["1496-4287"]},"external_id":{"arxiv":["2106.07328"],"isi":["001011963000001"]},"publication":"Canadian Mathematical Bulletin","author":[{"full_name":"Mohammadi, Ali","last_name":"Mohammadi","first_name":"Ali"},{"last_name":"Pham","first_name":"Thang","full_name":"Pham, Thang"},{"last_name":"Wang","first_name":"Yiting","id":"1917d194-076e-11ed-97cd-837255f88785","full_name":"Wang, Yiting","orcid":"0000-0002-2856-767X"}],"page":"1280-1295","doi":"10.4153/S000843952300036X","isi":1,"year":"2023","volume":66,"intvolume":"        66","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.07328"}],"abstract":[{"lang":"eng","text":"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\r\nM(|A|)=min{q4/3/|A|1/3(log|A|)2/3,|A|4/5/q13/5(log|A|)27/10}.\r\n 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).\r\n"}],"department":[{"_id":"GradSch"}],"issue":"4","publication_status":"published","date_published":"2023-12-01T00:00:00Z","date_updated":"2024-01-29T11:00:46Z","article_processing_charge":"No","month":"12","day":"01","type":"journal_article","status":"public","title":"An energy decomposition theorem for matrices and related questions","quality_controlled":"1","scopus_import":"1","publisher":"Cambridge University Press","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-06-11T22:00:40Z","oa_version":"Preprint","oa":1}