Baker A. Transcendental number theory (CUP， 1975)(K)(T)(155s)(1) .pdf

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1、TRANSCENDENTALNUMBERTHEORYALANBAKERf.r.s.FellowofTrinityCollege,CambridgeProfessorofPureMathematics,UniversityofCambridge*****CAMBRIDGEUNIVERSITYPRESSJPublishedbytheRyndioHofthnPAintiridgnTTnivorttityPressBentleyHouho,200KtmtonKomi,LondonNWI2DBAmericanBranch:32KuhIti

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3、stheorem2Transcendenceofe3Lindemann'stheorem2Linearformsinlogarithms1Introduction2Corollaries3Notation4Theauxiliaryfunction5Proofofmaintheorem3Lowerboundsforlinearforms1Introduction2Preliminaries3Theauxiliaryfunction4Proofofmaintheorem4,Diophantineequations1Introduct

4、ion2TheThueequation3Thehyperellipticequation4Curvesofgenus15Quantitativebounds5Classnumbersofimaginaryquadraticfields1Introduction2Z-functions3Limitformula4Classnumber15Classnumber2viCONTENTSEllipticfunctions1IntroductionjHtyi:552Corollaries5<>3Linearequations584Thea

5、uxiliaryfunction585Proofofmaintheorem606Periodsandquasi-periods61Rationalapproximationstoalgebraicnumbers1Introduction662Wronskians693Theindex694Acombinatoriallemma735Grids746Theauxiliarypolynomial757Successiveminima768Comparisonofminima799Exterioralgebra8110Proofofm

6、aintheorem82Mahler'sclassification1Introduction852A-numbers873Algebraicdependence884Heightsofpolynomials895^-numbers906[/-numbers907T-numbers92Metricaltheory1Introduction952Zerosofpolynomials963Nullsets984Intersectionsofintervals995Proofofmaintheorem10010Theexponenti

7、alfunction1Introduction103CONTENTSVii2Fundamentalpolynomialspage1043Proofofmaintheorem10811TheSiegel-Shidlovskytheorems1Introduction1092Basicconstruction1113Furtherlemmas1144Proofofmaintheorem11512Algebraicindependence1Introduction1182Exponentialpolynomials1203Height

8、s1224Algebraiccriterion1245Mainarguments125Bibliography129Originalpapers130Index145PREFACEFermat,Evler,Lagrange,Legendre...introitu