TheAlgorithmicNumberTheorySymposiabeganin1994atCornellUniversity inIthaca,NewYorktorecognizethegrowingimportanceofalgorithmicwork in the theory of numbers. The subject of the conference is broadly construed toencompassadiversebodyofmathematics,andtocoverboththetheoretical andpracticaladvancesinthe?eld. Theyhavebeenheldeverytwoyearssince: inBordeaux(Universit'eBordeauxI)in1996,Portland(ReedCollege)in1998, Leiden(UniversiteitLeiden)in2000,andthepresentconferencehostedbythe MagmaComputationalAlgebraGroupattheUniversityofSydney ...
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TheAlgorithmicNumberTheorySymposiabeganin1994atCornellUniversity inIthaca,NewYorktorecognizethegrowingimportanceofalgorithmicwork in the theory of numbers. The subject of the conference is broadly construed toencompassadiversebodyofmathematics,andtocoverboththetheoretical andpracticaladvancesinthe?eld. Theyhavebeenheldeverytwoyearssince: inBordeaux(Universit'eBordeauxI)in1996,Portland(ReedCollege)in1998, Leiden(UniversiteitLeiden)in2000,andthepresentconferencehostedbythe MagmaComputationalAlgebraGroupattheUniversityofSydney. TheconferenceprogramincludedinvitedtalksbyManjulBhargava(Prin- ton),JohnCoates(Cambridge),AntoineJoux(DCSSICryptoLab),BjornP- nen(Berkeley),andTakakazuSatoh(Saitama),aswellas34contributedtalks invariousareasofnumbertheory. Inadditiontothemathematicalprogram,the conferenceincludedaspecialdinnertohonourAlfvanderPoortenofMacquarie University,ontheoccasionofhis60thbirthday. Eachpaperwasreviewedbyatleasttwoexpertsexternaltotheprogram committeeandtheselectionofpaperswasmadeonthebasisoftheserec- mendations. Weexpressourappreciationtothe66expertrefereeswhoprovided reportsonaverytightschedule. Refereeingofthesubmissionfromamemberof theMagmagroupwasorganizedbyJoeBuhler. Theprogramcommitteethanksthegenerousadvicefromorganizersofpre- ousANTSconferences,particularlyJoeBuhler,WiebBosma,HendrikLenstra, andBartdeSmit. TheconferencewasgenerouslysupportedbytheCollegeof ScienceandTechnology,theSchoolofMathematicsandStatistics(bothatthe UniversityofSydney),theAustralianDefenceScienceTechnologyOrganisation, andeSign. April2002 JohnCannon ClausFieker DavidKohel TableofContents InvitedTalks GaussCompositionandGeneralizations ...1 ManjulBhargava EllipticCurves-TheCrossroadsofTheoryandComputation...9 JohnCoates TheWeilandTatePairingsasBuildingBlocks forPublicKeyCryptosystems...20 AntoineJoux UsingEllipticCurvesofRankOnetowardstheUndecidability ofHilbert'sTenthProblemoverRingsofAlgebraicIntegers...33 BjornPoonen Onp-adicPointCountingAlgorithmsforEllipticCurves overFiniteFields...43 TakakazuSatoh NumberTheory OnArithmeticallyEquivalentNumberFieldsofSmallDegree ...67 WiebBosma,BartdeSmit ASurveyofDiscriminantCounting...80 HenriCohen,FranciscoDiazyDiaz,MichelOlivier AHigher-RankMersenneProblem...95 GrahamEverest,PeterRogers,ThomasWard AnApplicationofSiegelModularFunctions toKronecker'sLimitFormula...108 TakashiFukuda,KeiichiKomatsu ComputationalAspectsofNUCOMP...1 20 MichaelJ. Jacobson,Jr. ,AlfredJ. vanderPoorten E?cientComputationofClassNumbersofRealAbelianNumberFields. . 134 St'ephaneR. Louboutin AnAcceleratedBuchmannAlgorithmforRegulatorComputation inRealQuadraticFields...148 UlrichVollmer VIII TableofContents ArithmeticGeometry SomeGenus3CurveswithManyPoints ...163 RolandAuer,JaapTop 7 8 Trinomialsax +bx+candax +bx+c withGaloisGroupsofOrder168and8*168...172 NilsBruin,NoamD. Elkies ComputationsonModularJacobianSurfaces...189 EnriqueGonz'alez-Jim'enez,JosepGonz'TheAlgorithmicNumberTheorySymposiabeganin1994atCornellUniversity inIthaca,NewYorktorecognizethegrowingimportanceofalgorithmicwork in the theory of numbers. The subject of the conference is broadly construed toencompassadiversebodyofmathematics,andtocoverboththetheoretical andpracticaladvancesinthe?eld. Theyhavebeenheldeverytwoyearssince: inBordeaux(Universit'eBordeauxI)in1996,Portland(ReedCollege)in1998, Leiden(UniversiteitLeiden)in2000,andthepresentconferencehostedbythe MagmaComputationalAlgebraGroupattheUniversityofSydney. TheconferenceprogramincludedinvitedtalksbyManjulBhargava(Prin- ton),JohnCoates(Cambridge),AntoineJoux(DCSSICryptoLab),BjornP- nen(Berkeley),andTakakazuSatoh(Saitama),aswellas34contributedtalks invariousareasofnumbertheory. Inadditiontothemathematicalprogram,the conferenceincludedaspecialdinnertohonourAlfvanderPoortenofMacquarie University,ontheoccasionofhis60thbirthday. Eachpaperwasreviewedbyatleasttwoexpertsexternaltotheprogram committeeandtheselectionofpaperswasmadeonthebasisoftheserec- mendations. Weexpressourappreciationtothe66expertrefereeswhoprovide
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Add this copy of Algorithmic Number Theory: 5th International Symposium, to cart. $34.25, very good condition, Sold by GuthrieBooks rated 4.0 out of 5 stars, ships from Spring Branch, TX, UNITED STATES, published 2002 by Springer.
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2002, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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Add this copy of Algorithmic Number Theory: 5th International Symposium, to cart. $73.82, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2002 by Springer.
Edition:
2002, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
