LEADER 03587nam 2200577 450 001 996466663603316 005 20220214124450.0 010 $a3-540-48083-8 024 7 $a10.1007/BFb0073786 035 $a(CKB)1000000000437159 035 $a(SSID)ssj0000321842 035 $a(PQKBManifestationID)12081109 035 $a(PQKBTitleCode)TC0000321842 035 $a(PQKBWorkID)10281035 035 $a(PQKB)10692022 035 $a(DE-He213)978-3-540-48083-9 035 $a(MiAaPQ)EBC5585742 035 $a(Au-PeEL)EBL5585742 035 $a(OCoLC)1066190393 035 $a(MiAaPQ)EBC6868059 035 $a(Au-PeEL)EBL6868059 035 $a(PPN)155190997 035 $a(EXLCZ)991000000000437159 100 $a20220214d1993 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aClassical diophantine equations /$fVladimir G. Sprindzuk 205 $a1st ed. 1993. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1993] 210 4$dİ1993 215 $a1 online resource (XII, 236 p.) 225 1 $aLecture Notes in Mathematics ;$vVolume 1559 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-57359-3 327 $aOrigins -- 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. 330 $aThe author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, now that the book appears in English, close studyand emulation. In particular those emphases allow him to devote the eighth chapter to an analysis of the interrelationship of the class number of algebraic number fields involved and the bounds on the heights of thesolutions of the diophantine equations. Those ideas warrant further development. The final chapter deals with effective aspects of the Hilbert Irreducibility Theorem, harkening back to earlier work of the author. There is no other congenial entry point to the ideas of the last two chapters in the literature. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vVolume 1559. 606 $aDiophantine equations 615 0$aDiophantine equations. 676 $a512.74 700 $aSprindzuk$b Vladimir G.$0441113 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466663603316 996 $aClassical Diophantine equations$978645 997 $aUNISA