{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:51:12Z","timestamp":1776840672730,"version":"3.51.2"},"reference-count":58,"publisher":"American Mathematical Society (AMS)","issue":"356","license":[{"start":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T00:00:00Z","timestamp":1769040000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["613.009.135"],"award-info":[{"award-number":["613.009.135"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We revisit Ito\u2019s [Osaka J. Math. 26 (1989), pp.\u00a0557\u2013578] natural extension of the Farey tent map, which generates all regular continued fraction convergents and mediants of a given irrational. With a slight shift in perspective on the order in which these convergents and mediants arise, this natural extension is shown to provide an elegant and powerful tool in the metric theory of continued fractions. A wealth of old and new results\u2014including limiting distributions of approximation coefficients, analogues of a theorem of Legendre and their refinements, and a generalisation of L\u00e9vy\u2019s Theorem to subsequences of convergents and mediants\u2014are presented as corollaries within this unifying theory.<\/p>","DOI":"10.1090\/mcom\/4046","type":"journal-article","created":{"date-parts":[[2024,11,20]],"date-time":"2024-11-20T10:46:20Z","timestamp":1732099580000},"page":"3101-3144","source":"Crossref","is-referenced-by-count":1,"title":["A unifying theory for metrical results on regular continued fraction convergents and mediants"],"prefix":"10.1090","volume":"94","author":[{"given":"Karma","family":"Dajani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cor","family":"Kraaikamp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Slade","family":"Sanderson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2025,1,22]]},"reference":[{"key":"1","unstructured":"Desmos, \\url{https:\/\/www.desmos.com}, Accessed: 2023-12-14."},{"issue":"5","key":"2","doi-asserted-by":"publisher","first-page":"2894","DOI":"10.1088\/1361-6544\/acc6b2","article-title":"On the topological entropy of (\ud835\udc4e,\ud835\udc4f)-continued fraction transformations","volume":"36","author":"Abrams, Adam","year":"2023","journal-title":"Nonlinearity","ISSN":"https:\/\/id.crossref.org\/issn\/0951-7715","issn-type":"print"},{"key":"3","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1515\/crll.1966.221.146","article-title":"Generalization of some classical theorems concerning triples of consecutive convergents to simple continued fractions","volume":"221","author":"Bagemihl, F.","year":"1966","journal-title":"J. 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