[{"publication_identifier":{"issn":["0933-7741"],"eissn":["1435-5337"]},"issue":"4","_id":"22190","OA_type":"green","intvolume":"        37","mathsc":["11C20","15B36","15B52"],"doi":"10.1515/forum-2024-0114","type":"journal_article","publication_status":"published","fulldoi":"https://doi.org/10.1515/forum-2024-0114","article_type":"original","article_processing_charge":"No","quality_controlled":"1","oa":1,"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We consider the set of 𝑚×𝑛 matrices with rational entries having numerator and denominator of size at most H and obtain various upper bounds on the number of such matrices of a given rank, or with a given determinant, or a given characteristic polynomial. We also consider similar questions for matrices whose entries are Egyptian fractions."}],"publisher":"De Gruyter","author":[{"full_name":"Afifurrahman, Muhammad","last_name":"Afifurrahman","first_name":"Muhammad"},{"last_name":"Kuperberg","first_name":"Vivian Zieve","full_name":"Kuperberg, Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697"},{"last_name":"Ostafe","first_name":"Alina","full_name":"Ostafe, Alina"},{"full_name":"Shparlinski, Igor E.","last_name":"Shparlinski","first_name":"Igor E."}],"citation":{"apa":"Afifurrahman, M., Kuperberg, V. Z., Ostafe, A., &#38; Shparlinski, I. E. (2024). Statistics of ranks, determinants and characteristic polynomials of rational matrices. <i>Forum Mathematicum</i>. De Gruyter. <a href=\"https://doi.org/10.1515/forum-2024-0114\">https://doi.org/10.1515/forum-2024-0114</a>","ieee":"M. Afifurrahman, V. Z. Kuperberg, A. Ostafe, and I. E. Shparlinski, “Statistics of ranks, determinants and characteristic polynomials of rational matrices,” <i>Forum Mathematicum</i>, vol. 37, no. 4. De Gruyter, 2024.","mla":"Afifurrahman, Muhammad, et al. “Statistics of Ranks, Determinants and Characteristic Polynomials of Rational Matrices.” <i>Forum Mathematicum</i>, vol. 37, no. 4, De Gruyter, 2024, doi:<a href=\"https://doi.org/10.1515/forum-2024-0114\">10.1515/forum-2024-0114</a>.","ista":"Afifurrahman M, Kuperberg VZ, Ostafe A, Shparlinski IE. 2024. Statistics of ranks, determinants and characteristic polynomials of rational matrices. Forum Mathematicum. 37(4).","ama":"Afifurrahman M, Kuperberg VZ, Ostafe A, Shparlinski IE. Statistics of ranks, determinants and characteristic polynomials of rational matrices. <i>Forum Mathematicum</i>. 2024;37(4). doi:<a href=\"https://doi.org/10.1515/forum-2024-0114\">10.1515/forum-2024-0114</a>","short":"M. Afifurrahman, V.Z. Kuperberg, A. Ostafe, I.E. Shparlinski, Forum Mathematicum 37 (2024).","chicago":"Afifurrahman, Muhammad, Vivian Zieve Kuperberg, Alina Ostafe, and Igor E. Shparlinski. “Statistics of Ranks, Determinants and Characteristic Polynomials of Rational Matrices.” <i>Forum Mathematicum</i>. De Gruyter, 2024. <a href=\"https://doi.org/10.1515/forum-2024-0114\">https://doi.org/10.1515/forum-2024-0114</a>."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2401.10086"}],"date_created":"2026-06-29T12:55:47Z","status":"public","title":"Statistics of ranks, determinants and characteristic polynomials of rational matrices","volume":37,"date_updated":"2026-07-14T10:48:41Z","oa_version":"Preprint","OA_place":"repository","date_published":"2024-01-01T00:00:00Z","arxiv":1,"month":"01","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","extern":"1","publication":"Forum Mathematicum","external_id":{"arxiv":["2401.10086"]}}]