Franklin

Local zeta functions attached to the minimal spherical series for a class of symmetric spaces / Nicole Bopp, Hubert Rubenthaler.

Author/Creator:
Bopp, Nicole, 1947- author.
Publication:
Providence, Rhode Island : American Mathematical Society, [2005]
Format/Description:
Book
1 online resource (250 p.)
Series:
Memoirs of the American Mathematical Society ; no. 821.
Memoirs of the American Mathematical Society, 0065-9266 ; number 821
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Subjects:
Functions, Zeta.
Symmetric spaces.
Form/Genre:
Electronic books.
Language:
English
Contents:
""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 Σ""; ""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 Î?[sub(0)]""; ""1.12. The case k = 0""; ""1.13. Properties of Î?[sub(0)]""
""1.14. The polynomials Î?[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 λ[sub(i)] and λ[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 Gâ€?orbits for Type I""; ""2.11. The classification""
""4.2. Two diffeomorphisms""""4.3. Isomorphisms between g(1), g (�1), V[sup(+)]( l ) and V[sup(-)](�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(+)])""
""6.5. Explicit functional equation for k = 0""
Notes:
"Volume 174, number 821 (first of 4 numbers)."
Includes bibliographical references (pages 227-230) and index.
Description based on print version record.
Contributor:
Rubenthaler, H. (Hubert), author.
ISBN:
1-4704-0422-2