{"product_id":"9783540573593","title":"Lecture Notes in Mathematics","description":"\u003ch1\u003eLecture Notes in Mathematics\u003c\/h1\u003e \u003ch2\u003eSprindzuk, Vladimir G.\u003c\/h2\u003e \u003cp\u003eThe author had initiated a revision and translation of\n\"Classical           Diophantine Equations\" prior to his death.\nGiven the rapid advances in      transcendence theory and\ndiophantine approximation over recent years, one   might fear\nthat the present work, originally published in Russian           in\n1982, is mostly superseded. That is not so. A certain amount\nof      updating had been prepared by the author himself before\nhis untimely death. Some further revision was prepared by\nclose colleagues.\nThe first seven chapters provide a detailed, virtually\nexhaustive, discussion of the theory of lower bounds for\nlinear forms in the logarithms of algebraic numbers and its\napplications to obtaining upper bounds for solutions to                 the\neponymous classical diophantine equations. The detail may\nseem stark--- the author fears that the reader may react\nmuch as does the tourist on  first seeing the centre\nPompidou; notwithstanding that, Sprind zuk maintainsa\npleasant and chatty approach, full of wise and interesting\nremarks.   His emphases well warrant, now that the book\nappears in English, close studyand emulation. In particular\nthose emphases allow him to devote the eighth  chapter to an\nanalysis of the interrelationship of the class number         of\nalgebraic number fields involved and the bounds on the\nheights of thesolutions of the diophantine equations. Those\nideas warrant further         development. The final chapter deals\nwith effective aspects of the Hilbert  Irreducibility\nTheorem, harkening back to earlier work of the author.       There\nis no other congenial entry point to the ideas of the last\ntwo    chapters in the literature.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1993-12-20\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540573593\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/BFb0073786\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 236\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":45369779978380,"sku":"9783540573593","price":62.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540573593.jpg?v=1775674916","url":"https:\/\/lateknightbooks.com\/products\/9783540573593","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}