{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T11:06:23Z","timestamp":1780657583171,"version":"3.54.1"},"reference-count":20,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Finite Fields and Their Applications"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.ffa.2026.102858","type":"journal-article","created":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T10:16:10Z","timestamp":1780654570000},"page":"102858","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Cubic Pell equations over polynomial rings and superelliptic curves y3\u202f=\u202fx3n\u202f+\u202fax\u202f+\u202fb"],"prefix":"10.1016","volume":"115","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0996-8910","authenticated-orcid":false,"given":"Tomasz","family":"J\u0119drzejak","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.ffa.2026.102858_br0010","doi-asserted-by":"crossref","DOI":"10.1007\/b97610","article-title":"Pell's Equation","author":"Barbeau","year":"2003"},{"key":"10.1016\/j.ffa.2026.102858_br0020","article-title":"Neverending Fractions. An Introduction to Continued Fractions","volume":"vol. 23","author":"Borwein","year":"2014"},{"issue":"3\u20134","key":"10.1016\/j.ffa.2026.102858_br0030","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/jsco.1996.0125","article-title":"The Magma algebra system. I. The user language","volume":"24","author":"Bosma","year":"1997","journal-title":"J. Symb. Comput."},{"issue":"9","key":"10.1016\/j.ffa.2026.102858_br0040","first-page":"491","article-title":"Formes cubiques polynomiales","volume":"311","author":"Gaunet","year":"1990","journal-title":"C. R. Acad. Sci. Paris, Ser. I Math."},{"key":"10.1016\/j.ffa.2026.102858_br0050","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/0024-3795(84)90089-2","article-title":"On the discriminant of a trinomial","volume":"62","author":"Greenfield","year":"1984","journal-title":"Linear Algebra Appl."},{"issue":"237","key":"10.1016\/j.ffa.2026.102858_br0060","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1090\/S0025-5718-00-01297-7","article-title":"Arithmetic on superelliptic curves","volume":"71","author":"Galbraith","year":"2002","journal-title":"Math. Comput."},{"issue":"1","key":"10.1016\/j.ffa.2026.102858_br0070","doi-asserted-by":"crossref","first-page":"9","DOI":"10.4064\/aa-48-1-9-47","article-title":"Unit\u00e9s de certains sous-anneaux des corps de fonctions alg\u00e9briques","volume":"48","author":"Hellegouarch","year":"1987","journal-title":"Acta Arith."},{"key":"10.1016\/j.ffa.2026.102858_br0080","article-title":"Diophantine Geometry","volume":"vol. 201","author":"Hindry","year":"2000"},{"key":"10.1016\/j.ffa.2026.102858_br0090","doi-asserted-by":"crossref","first-page":"143","DOI":"10.4064\/bc108-0-11","article-title":"A note on the torsion of the Jacobians of superelliptic curves yq=xp+a","volume":"108","author":"J\u0119drzejak","year":"2016","journal-title":"Banach Cent. Publ."},{"issue":"2","key":"10.1016\/j.ffa.2026.102858_br0100","first-page":"263","article-title":"Polynomial Pell equations P(x)2\u2212(x2m+ax+b)Q(x)2=1 and associated hyperelliptic curves","volume":"34","author":"J\u0119drzejak","year":"2019","journal-title":"J. Ramanujan Math. Soc."},{"key":"10.1016\/j.ffa.2026.102858_br0210","doi-asserted-by":"crossref","DOI":"10.1142\/S1793042126500909","article-title":"Polynomial Pell equations with D(x)=x6+ax2+b","author":"J\u0119drzejak","year":"2026","journal-title":"Int. J. Number Theory"},{"key":"10.1016\/j.ffa.2026.102858_br0120","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.jnt.2013.11.011","article-title":"Variations on twists of tuples of hyperelliptic curves and related results","volume":"137","author":"J\u0119drzejak","year":"2014","journal-title":"J. Number Theory"},{"issue":"1","key":"10.1016\/j.ffa.2026.102858_br0130","doi-asserted-by":"crossref","first-page":"107","DOI":"10.51286\/albjm\/1575612673","article-title":"From hyperelliptic to superelliptic curves","volume":"13","author":"Malmendier","year":"2019","journal-title":"Albanian J. Math."},{"key":"10.1016\/j.ffa.2026.102858_br0140","doi-asserted-by":"crossref","first-page":"2379","DOI":"10.4171\/jems\/560","article-title":"Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings","volume":"17","author":"Masser","year":"2015","journal-title":"J. Eur. Math. Soc."},{"issue":"3","key":"10.1016\/j.ffa.2026.102858_br0150","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1007\/s11139-019-00233-1","article-title":"A note on the use of R\u00e9dei polynomials for solving the polynomial Pell equation and its generalization to higher degrees","volume":"53","author":"Murru","year":"2020","journal-title":"Ramanujan J."},{"issue":"1","key":"10.1016\/j.ffa.2026.102858_br0160","first-page":"89","article-title":"Polynomial Pell's equations","volume":"56","author":"Nathanson","year":"1976","journal-title":"Proc. Am. Math. Soc."},{"key":"10.1016\/j.ffa.2026.102858_br0170","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.jnt.2023.12.009","article-title":"Quartic integral polynomial Pell equations","volume":"259","author":"Scherr","year":"2024","journal-title":"J. Number Theory"},{"issue":"4","key":"10.1016\/j.ffa.2026.102858_br0180","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1090\/S0002-9939-02-06934-4","article-title":"Polynomial Pell's equation","volume":"131","author":"Webb","year":"2003","journal-title":"Proc. Am. Math. Soc."},{"issue":"1","key":"10.1016\/j.ffa.2026.102858_br0190","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.jnt.2003.12.005","article-title":"Polynomial Pell's equation II","volume":"106","author":"Webb","year":"2004","journal-title":"J. Number Theory"},{"key":"10.1016\/j.ffa.2026.102858_br0200","series-title":"Trends in Contemporary Mathematics","first-page":"151","article-title":"Unlikely intersections and Pell's equations in polynomials","volume":"vol. 8","author":"Zannier","year":"2014"}],"container-title":["Finite Fields and Their Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1071579726000699?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1071579726000699?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T10:16:13Z","timestamp":1780654573000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1071579726000699"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":20,"alternative-id":["S1071579726000699"],"URL":"https:\/\/doi.org\/10.1016\/j.ffa.2026.102858","relation":{},"ISSN":["1071-5797"],"issn-type":[{"value":"1071-5797","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Cubic Pell equations over polynomial rings and superelliptic curves y3\u202f=\u202fx3n\u202f+\u202fax\u202f+\u202fb","name":"articletitle","label":"Article Title"},{"value":"Finite Fields and Their Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ffa.2026.102858","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"102858"}}