FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1967973885> ?p ?o ?g. }

• W1967973885 endingPage "543" @default.
• W1967973885 startingPage "513" @default.
• W1967973885 abstract "We investigate integer solutions of the superelliptic equation z m = F ( x , y ) , ((1)) where F is a homogeneous polynomial with integer coefficients, and of the generalized Fermat equation A x p + B y q = C z r , ((2)) where A, B and C are non-zero integers. Call an integer solution (x, y, z) to such an equation proper if gcd(x, y, z) = 1. Using Faltings' Theorem, we shall give criteria for these equations to have only finitely many proper solutions. We examine (1) using a descent technique of Kummer, which allows us to obtain, from any infinite set of proper solutions to (1), infinitely many rational points on a curve of (usually) high genus, thus contradicting Faltings' Theorem (for example, this works if F(t, 1) = 0 has three simple roots and m ⩾ 4). We study (2) via a descent method which uses unramified coverings of P1 {0, 1, ∞} of signature (p, q, r), and show that (2) has only finitely many proper solutions if l/p + l/q + 1/r < 1. In cases where these coverings arise from modular curves, our descent leads naturally to the approach of Hellegouarch and Frey to Fermat's Last Theorem. We explain how their idea may be exploited for other examples of (2). We then collect together a variety of results for (2) when 1/p + 1/q + 1/r ⩾ 1. In particular, we consider ‘local-global’ principles for proper solutions, and consider solutions in function fields." @default.
• W1967973885 created "2016-06-24" @default.
• W1967973885 creator A5019320081 @default.
• W1967973885 creator A5066205389 @default.
• W1967973885 date "1995-11-01" @default.
• W1967973885 modified "2023-10-04" @default.
• W1967973885 title "On the Equations <i>z^m </i> = <i>F</i> (<i>x, y</i> ) and <i>Ax^p </i> + <i>By^q </i> = <i>Cz^r </i>" @default.
• W1967973885 cites W1575761830 @default.
• W1967973885 cites W2006077852 @default.
• W1967973885 cites W2008147755 @default.
• W1967973885 cites W2049806477 @default.
• W1967973885 cites W2078035743 @default.
• W1967973885 cites W2115624046 @default.
• W1967973885 cites W2402433754 @default.
• W1967973885 cites W2798483379 @default.
• W1967973885 cites W3155754291 @default.
• W1967973885 cites W97355986 @default.
• W1967973885 doi "https://doi.org/10.1112/blms/27.6.513" @default.
• W1967973885 hasPublicationYear "1995" @default.
• W1967973885 type Work @default.
• W1967973885 sameAs 1967973885 @default.
• W1967973885 citedByCount "124" @default.
• W1967973885 countsByYear W19679738852012 @default.
• W1967973885 countsByYear W19679738852013 @default.
• W1967973885 countsByYear W19679738852014 @default.
• W1967973885 countsByYear W19679738852015 @default.
• W1967973885 countsByYear W19679738852016 @default.
• W1967973885 countsByYear W19679738852017 @default.
• W1967973885 countsByYear W19679738852018 @default.
• W1967973885 countsByYear W19679738852019 @default.
• W1967973885 countsByYear W19679738852020 @default.
• W1967973885 countsByYear W19679738852021 @default.
• W1967973885 countsByYear W19679738852022 @default.
• W1967973885 countsByYear W19679738852023 @default.
• W1967973885 crossrefType "journal-article" @default.
• W1967973885 hasAuthorship W1967973885A5019320081 @default.
• W1967973885 hasAuthorship W1967973885A5066205389 @default.
• W1967973885 hasConcept C114614502 @default.
• W1967973885 hasConcept C118615104 @default.
• W1967973885 hasConcept C121332964 @default.
• W1967973885 hasConcept C134306372 @default.
• W1967973885 hasConcept C138885662 @default.
• W1967973885 hasConcept C14036430 @default.
• W1967973885 hasConcept C153294291 @default.
• W1967973885 hasConcept C157369684 @default.
• W1967973885 hasConcept C199360897 @default.
• W1967973885 hasConcept C2776637919 @default.
• W1967973885 hasConcept C2780813799 @default.
• W1967973885 hasConcept C33923547 @default.
• W1967973885 hasConcept C41008148 @default.
• W1967973885 hasConcept C41895202 @default.
• W1967973885 hasConcept C59822182 @default.
• W1967973885 hasConcept C78458016 @default.
• W1967973885 hasConcept C86803240 @default.
• W1967973885 hasConcept C87670640 @default.
• W1967973885 hasConcept C90119067 @default.
• W1967973885 hasConcept C97137487 @default.
• W1967973885 hasConceptScore W1967973885C114614502 @default.
• W1967973885 hasConceptScore W1967973885C118615104 @default.
• W1967973885 hasConceptScore W1967973885C121332964 @default.
• W1967973885 hasConceptScore W1967973885C134306372 @default.
• W1967973885 hasConceptScore W1967973885C138885662 @default.
• W1967973885 hasConceptScore W1967973885C14036430 @default.
• W1967973885 hasConceptScore W1967973885C153294291 @default.
• W1967973885 hasConceptScore W1967973885C157369684 @default.
• W1967973885 hasConceptScore W1967973885C199360897 @default.
• W1967973885 hasConceptScore W1967973885C2776637919 @default.
• W1967973885 hasConceptScore W1967973885C2780813799 @default.
• W1967973885 hasConceptScore W1967973885C33923547 @default.
• W1967973885 hasConceptScore W1967973885C41008148 @default.
• W1967973885 hasConceptScore W1967973885C41895202 @default.
• W1967973885 hasConceptScore W1967973885C59822182 @default.
• W1967973885 hasConceptScore W1967973885C78458016 @default.
• W1967973885 hasConceptScore W1967973885C86803240 @default.
• W1967973885 hasConceptScore W1967973885C87670640 @default.
• W1967973885 hasConceptScore W1967973885C90119067 @default.
• W1967973885 hasConceptScore W1967973885C97137487 @default.
• W1967973885 hasIssue "6" @default.
• W1967973885 hasLocation W19679738851 @default.
• W1967973885 hasOpenAccess W1967973885 @default.
• W1967973885 hasPrimaryLocation W19679738851 @default.
• W1967973885 hasRelatedWork W1998559239 @default.
• W1967973885 hasRelatedWork W2012013824 @default.
• W1967973885 hasRelatedWork W2018825381 @default.
• W1967973885 hasRelatedWork W2360587676 @default.
• W1967973885 hasRelatedWork W2384888244 @default.
• W1967973885 hasRelatedWork W2610734521 @default.
• W1967973885 hasRelatedWork W2963754092 @default.
• W1967973885 hasRelatedWork W3033936578 @default.
• W1967973885 hasRelatedWork W3041670244 @default.
• W1967973885 hasRelatedWork W4301262132 @default.
• W1967973885 hasVolume "27" @default.
• W1967973885 isParatext "false" @default.
• W1967973885 isRetracted "false" @default.
• W1967973885 magId "1967973885" @default.
• W1967973885 workType "article" @default.