03587nam 2200577 450 99646666360331620220214124450.03-540-48083-810.1007/BFb0073786(CKB)1000000000437159(SSID)ssj0000321842(PQKBManifestationID)12081109(PQKBTitleCode)TC0000321842(PQKBWorkID)10281035(PQKB)10692022(DE-He213)978-3-540-48083-9(MiAaPQ)EBC5585742(Au-PeEL)EBL5585742(OCoLC)1066190393(MiAaPQ)EBC6868059(Au-PeEL)EBL6868059(PPN)155190997(EXLCZ)99100000000043715920220214d1993 uy 0engurnn|008mamaatxtccrClassical diophantine equations /Vladimir G. Sprindzuk1st ed. 1993.Berlin ;Heidelberg :Springer-Verlag,[1993]©19931 online resource (XII, 236 p.) Lecture Notes in Mathematics ;Volume 1559Bibliographic Level Mode of Issuance: Monograph3-540-57359-3 Origins -- Algebraic foundations -- Linear forms in the logarithms of algebraic numbers -- The Thue equation -- The Thue-Mahler equation -- Elliptic and hyperelliptic equations -- Equations of hyperelliptic type -- The class number value problem -- Reducibility of polynomials and diophantine equations.The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, now that the book appears in English, close studyand emulation. In particular those emphases allow him to devote the eighth chapter to an analysis of the interrelationship of the class number of algebraic number fields involved and the bounds on the heights of thesolutions of the diophantine equations. Those ideas warrant further development. The final chapter deals with effective aspects of the Hilbert Irreducibility Theorem, harkening back to earlier work of the author. There is no other congenial entry point to the ideas of the last two chapters in the literature.Lecture notes in mathematics (Springer-Verlag) ;Volume 1559.Diophantine equationsDiophantine equations.512.74Sprindzuk Vladimir G.441113MiAaPQMiAaPQMiAaPQBOOK996466663603316Classical Diophantine equations78645UNISA00783nam0 2200289 450 991102848000332120250930125634.0978889598290920250930d2025----km y0itay50 baitaITa 001yyElementi di Calcolo ApplicatoGiuseppe Dattoli,Elio Sabia1 ed.RomaTexmat2025c405 p.ill.24 cmAnalisi matematica51522itaDattoli,Giuseppe77355SabiaElio1849032ITUNINAREICATUNIMARCBK9911028480003321515-DAT-1253/2025SC1SC1Elementi di Calcolo Applicato4438039UNINA