LEADER 03706nam 2200601 450 001 9910480099303321 005 20180613001305.0 010 $a1-4704-0422-2 035 $a(CKB)3360000000465005 035 $a(EBL)3114239 035 $a(SSID)ssj0000973312 035 $a(PQKBManifestationID)11552361 035 $a(PQKBTitleCode)TC0000973312 035 $a(PQKBWorkID)10960111 035 $a(PQKB)10828997 035 $a(MiAaPQ)EBC3114239 035 $a(PPN)195417097 035 $a(EXLCZ)993360000000465005 100 $a20041027h20052005 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLocal zeta functions attached to the minimal spherical series for a class of symmetric spaces /$fNicole Bopp, Hubert Rubenthaler 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2005] 210 4$d©2005 215 $a1 online resource (250 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 821 300 $a"Volume 174, number 821 (first of 4 numbers)." 311 $a0-8218-3623-4 320 $aIncludes bibliographical references (pages 227-230) and index. 327 $a""Table of Contents""; ""Introduction""; ""Chapter 1. A Class of Real Prehomogeneous Spaces""; ""1.1. A class of graded algebras""; ""1.2. Root systems""; ""1.3. Complexification""; ""1.4. Highest root in I?£""; ""1.5. The first step for the descent""; ""1.6. The descent""; ""1.7. Generic elements in V[sup(+)]""; ""1.8. Structure of the regular graded algebra (g, H[sub(0)])""; ""1.9. Properties of the spaces E[sub(i,j)] (p, q)""; ""1.10. Normalization of the Killing form""; ""1.11. The relative invariant I??[sub(0)]""; ""1.12. The case k = 0""; ""1.13. Properties of I??[sub(0)]"" 327 $a""1.14. The polynomials I??[sub(j)]""""Chapter 2. The Orbits of G in V[sup(+)]""; ""2.1. Representations of sl( 2, C)""; ""2.2. First reduction""; ""2.3. An involution which permutes the roots in E[sub(i,j)(+1,+1)""; ""2.4. Construction of elements interchanging I?»[sub(i)] and I?»[sub(j)]""; ""2.5. Quadratic forms""; ""2.6. The G-orbits for Type III""; ""2.7. The G-orbits for Type II""; ""2.8. Signature of the quadratic forms qx[sub(i)],x[sub(j)]""; ""2.9. Action of Z[sub(G)](I[sup(+)]) for Type I""; ""2.10. The Ga???orbits for Type I""; ""2.11. The classification"" 327 $a""4.2. Two diffeomorphisms""""4.3. Isomorphisms between g(1), g (a???1), V[sup(+)]( l ) and V[sup(-)](a???1)""; ""4.4. A first normalization and its consequence""; ""4.5. A second normalization and its consequence""; ""4.6. Integral formulas on V[sup(+)] and V[sup(-)]""; ""4.7. Fourier transform of a quadratic character""; ""4.8. A relation between T[sup(-)][sub(Ff)] and T[sup(+)][sub(f)]""; ""Chapter 5. Functional Equation of the Zeta Functionfor Type I and II""; ""5.1. Definition of the local Zeta functions""; ""5.2. Existence of a functional equation for (AN, V[sup(+)])"" 327 $a""6.5. Explicit functional equation for k = 0"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 821. 606 $aFunctions, Zeta 606 $aSymmetric spaces 608 $aElectronic books. 615 0$aFunctions, Zeta. 615 0$aSymmetric spaces. 676 $a510 s 676 $a515/.56 700 $aBopp$b Nicole$f1947-$0950403 702 $aRubenthaler$b H$g(Hubert), 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480099303321 996 $aLocal zeta functions attached to the minimal spherical series for a class of symmetric spaces$92148800 997 $aUNINA