{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T12:26:20Z","timestamp":1774959980648,"version":"3.50.1"},"reference-count":80,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,26]],"date-time":"2025-01-26T00:00:00Z","timestamp":1737849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The aim of this paper is an exposition of fields of multiply periodic, or Kleinian, \u2118-functions. Such a field arises on the Jacobian variety of an algebraic curve, providing natural algebraic models for the Jacobian and Kummer varieties, possessing the addition law, and accommodating dynamical equations with solutions. All of this will be explained in detail for plane algebraic curves in their canonical forms. Examples of hyperelliptic and non-hyperelliptic curves are presented.<\/jats:p>","DOI":"10.3390\/axioms14020090","type":"journal-article","created":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T08:57:48Z","timestamp":1738054668000},"page":"90","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Abelian Function Fields on Jacobian Varieties"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8175-8846","authenticated-orcid":false,"given":"Julia","family":"Bernatska","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Connecticut, 341 Mansfield Rd., Storrs, CT 06269, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Baker, H.F. (1897). 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