{"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":66,"year":"2023","department":[{"_id":"GradSch"}],"isi":1,"abstract":[{"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","lang":"eng"}],"quality_controlled":"1","issue":"4","type":"journal_article","intvolume":"        66","title":"An energy decomposition theorem for matrices and related questions","article_type":"original","doi":"10.4153/S000843952300036X","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>.","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>.","short":"A. Mohammadi, T. Pham, Y. Wang, Canadian Mathematical Bulletin 66 (2023) 1280–1295.","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>","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>","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."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.07328"}],"date_updated":"2024-01-29T11:00:46Z","article_processing_charge":"No","date_published":"2023-12-01T00:00:00Z","publication_status":"published","publication_identifier":{"eissn":["1496-4287"],"issn":["0008-4395"]},"month":"12","oa_version":"Preprint","author":[{"last_name":"Mohammadi","full_name":"Mohammadi, Ali","first_name":"Ali"},{"last_name":"Pham","full_name":"Pham, Thang","first_name":"Thang"},{"last_name":"Wang","first_name":"Yiting","id":"1917d194-076e-11ed-97cd-837255f88785","full_name":"Wang, Yiting","orcid":"0000-0002-2856-767X"}],"publisher":"Cambridge University Press","language":[{"iso":"eng"}],"external_id":{"isi":["001011963000001"],"arxiv":["2106.07328"]},"page":"1280-1295","date_created":"2023-06-11T22:00:40Z","scopus_import":"1","publication":"Canadian Mathematical Bulletin","_id":"13128","status":"public","day":"01"}