LEADER 05399nam 2200685Ia 450 001 9910806985203321 005 20240313233846.0 010 $a1-281-92483-0 010 $a9786611924836 010 $a981-277-353-3 035 $a(CKB)1000000000552098 035 $a(EBL)1214921 035 $a(SSID)ssj0000345214 035 $a(PQKBManifestationID)12087605 035 $a(PQKBTitleCode)TC0000345214 035 $a(PQKBWorkID)10323242 035 $a(PQKB)10544237 035 $a(MiAaPQ)EBC1214921 035 $a(WSP)00006115 035 $a(Au-PeEL)EBL1214921 035 $a(CaPaEBR)ebr10699070 035 $a(CaONFJC)MIL192483 035 $a(OCoLC)854973178 035 $a(EXLCZ)991000000000552098 100 $a20060926d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aArithmetic geometry and number theory /$feditors, Lin Weng, Iku Nakamura 205 $a1st ed. 210 $aHackensack, NJ $cWorld Scientific$dc2006 215 $a1 online resource (411 p.) 225 0 $aSeries on number theory and its applications ;$vv. 1 300 $aDescription based upon print version of record. 311 $a981-256-814-X 320 $aIncludes bibliographical references. 327 $aForeword; Preface; Contents; On Local y-Factors; 1 Introduction; 2 Basic Properties of Local y-Factors; 2.1 Multiplicativity; 2.2 Stability; 2.3 Remarks; 3 Local Converse Theorems; 3.1 The case of GLn(F); 3.2 A conjectural LCT; 3.3 The case of SO2n+1(F); 4 Poles of Local y-Factors; 4.1 The case of G = SO2n+1; 4.2 Other classical groups; Deligne Pairings over Moduli Spaces of Punctured Riemann Surfaces; 1 WP Metrics and TZ Metrics; 2 Line Bundles over Moduli Spaces; 3 Fundamental Relations on MgN' Algebraic Story; 4 Fundamental Relation on MgN- Arithmetic Story; 5 Deligne Tuple in General 327 $a6 Degeneration of TZ Metrics: Analytic StoryReferences; Vector Bundles on Curves over Cp; 1 Introduction; 2 Complex Vector Bundles; 3 Fundamental Groups of p-Adic Curves; 4 Finite Vector Bundles; 5 A Bigger Category of Vector Bundles; 6 Parallel Transport on Bundles in Bxcp; 7 Working Outside a Divisor on Xcp; 8 Properties of Parallel Transport; 9 Semistable Bundles; 10 A Simpler Description of Bxcp D; 11 Strongly Semistable Reduction; 12 How Big are our Categories of Bundles?; 13 Representations of the Fundamental Group; 14 Mumford Curves; References 327 $aAbsolute CM-periods -- Complex and p-Adic1 Introduction; 2 Notation; 2.1 Complex Theory; 2.2 p-Adic Theory; References; Special Zeta Values in Positive Characteristic; 1 Introduction; 2 Carlitz Theory; 3 Anderson-Thakur Theory; 4 t-Motives; 5 Algebraic Independence of the Special Zeta Values; References; Automorphic Forms & Eisenstein Series and Spectral Decompositions; Day One: Basics of Automorphic Forms; 1 Basic Decompositions; 1.1 Langlands Decomposition; 1.2 Reduction Theory: Siegel Sets; 1.3 Moderate Growth and Rapidly Decreasing; 1.4 Automorphic Forms; 2 Structural Results 327 $a2.1 Moderate Growth and Rapid Decreasing2.2 Semi-Simpleness; 2.3 3-Finiteness; 2.4 Philosophy of Cusp Forms; 2.5 L2-Automorphic Forms; Day Two: Eisenstein Series; 3 Definition; 3.1 Equivalence Classes of Automorphic Representations; 3.2 Eisenstein Series and Intertwining Operators; 3.3 Convergence; 4 Constant Terms of Eisenstein Series; 5 Fundamental Properties of Eisenstein Series; Day Three: Pseudo-Eisenstein Series; 6 Paley-Wiener Functions; 6.1 Paley-Wiener Functions; 6.2 Fourier Transforms; 6.3 Paley-Wiener on p; 7 Pseudo-Eisenstein Series; 8 First Decomposition of L2(G(F)\G(A))\ 327 $a8.1 Inner Product Formula for P-ESes8.2 Decomposition of L2-Spaces According to Cuspidal Data; 8.3 Constant Terms of P-SEes; 9 Decomposition of Automorphic Forms According to Cuspidal Data; 9.1 Main Result; 9.2 Langlands Operators; 9.3 Key Bridge; Day Four: Spectrum Decomposition: Residual Process; 10 Why Residue?; 10.1 Pseudo-Eisenstein Series and Residual Process; 10.2 What do we have?; 10.3 Difficulties; 11 Main Results; 11.1 Functional Analysis; 11.2 Main Theorem: Rough Version; 11.3 Main Theorem: Refined Version; 11.4 How to Prove? 327 $aDay Five: Eisenstein Systems and Spectral Decomposition (II) 330 $aMathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of specia 410 0$aSeries on Number Theory & Its Applications 606 $aNumber theory 606 $aAlgebra 615 0$aNumber theory. 615 0$aAlgebra. 676 $a512.7 701 $aWeng$b Lin$f1964-$01651918 701 $aNakamura$b Iku$01651919 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910806985203321 996 $aArithmetic geometry and number theory$94002197 997 $aUNINA