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020 _a9783540480839
_9978-3-540-48083-9
024 7 _a10.1007/BFb0073786
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
072 7 _aPBH
_2thema
082 0 4 _a512.7
_223
100 1 _aSprindžuk, Vladimir G.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aClassical Diophantine Equations
_h[electronic resource] /
_cby Vladimir G. Sprindžuk ; edited by Ross Talent.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1993.
300 _aXII, 236 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLOMI and Euler International Mathematical Institute, St.Petersburg ;
_v1559
505 0 _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.
520 _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over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded.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.
650 0 _aNumber theory.
650 1 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
700 1 _aTalent, Ross.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662182864
776 0 8 _iPrinted edition:
_z9783540573593
830 0 _aLOMI and Euler International Mathematical Institute, St.Petersburg ;
_v1559
856 4 0 _uhttps://doi.org/10.1007/BFb0073786
912 _aZDB-2-SMA
912 _aZDB-2-LNM
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