a window into zeta and modular physics mathematical sciences research institute publications外语英文电子书

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1、Thisbookprovidesanintroduction,withapplications,tothreeinterconnectedmathematicaltopics:•zetafunctionsintheirrichvariety:thoseofRiemann,Hurwitz,Barnes,Epstein,Selberg,andRuelle,plusgraphzetafunctions;•modularforms:Eisensteinseries,HeckeandDirichletL-functions,Ra-manujan’stauf

2、unction,andcuspforms;•vertexoperatoralgebras:correlationfunctions,quasimodularforms,mod-ularinvariance,rationality,andsomecurrentresearchtopicsincludinghigher-genusconformalfieldtheory.Applicationsofthematerialtophysicsarepresented,includingKaluza–Kleinextra-dimensionalgravity

3、,bosonicstringcalculations,aCardyformulaforblackholeentropy,Patterson–Selbergzetafunctionexpressionsofone-loopquantumfieldandgravitypartitionfunctions,Casimirenergycalculations,atomicSchr¨odingeroperators,Bose–Einsteincondensation,heatkernelasymp-totics,randommatrices,quantumc

4、haos,ellipticandthetafunctionsolutionsofEinstein’sequations,asoliton–blackholeconnectionintwo-dimensionalgravity,andconformalfieldtheory.MathematicalSciencesResearchInstitutePublications57AWindowintoZetaandModularPhysicsMathematicalSciencesResearchInstitutePublications1Freed/U

5、hlenbeck:InstantonsandFour-Manifolds,secondedition2Chern(ed.):SeminaronNonlinearPartialDifferentialEquations3Lepowsky/Mandelstam/Singer(eds.):VertexOperatorsinMathematicsandPhysics4Kac(ed.):InfiniteDimensionalGroupswithApplications5Blackadar:K-TheoryforOperatorAlgebras,seconded

6、ition6Moore(ed.):GroupRepresentations,ErgodicTheory,OperatorAlgebras,andMathematicalPhysics7Chorin/Majda(eds.):WaveMotion:Theory,Modelling,andComputation8Gersten(ed.):EssaysinGroupTheory9Moore/Schochet:GlobalAnalysisonFoliatedSpaces,secondedition10–11Drasin/Earle/Gehring/Kra/

7、Marden(eds.):HolomorphicFunctionsandModuli12–13Ni/Peletier/Serrin(eds.):NonlinearDiffusionEquationsandTheirEquilibriumStates14Goodman/delaHarpe/Jones:CoxeterGraphsandTowersofAlgebras15Hochster/Huneke/Sally(eds.):CommutativeAlgebra16Ihara/Ribet/Serre(eds.):GaloisGroupsoverQ17Co

8、ncus/Finn/Hoffman(eds.):GeometricAnalysisandComputerGraphics18Bryant/