Buch, Englisch, 168 Seiten, Format (B × H): 216 mm x 279 mm, Gewicht: 487 g
Reihe: Frontiers in Mathematics
Buch, Englisch, 168 Seiten, Format (B × H): 216 mm x 279 mm, Gewicht: 487 g
Reihe: Frontiers in Mathematics
ISBN: 978-3-7643-7059-6
Verlag: Springer
This book describes the basic theory of hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces.
Hypercomplex analyticity generalizes the concept of complex analyticity in the sense of considering null-solutions to higher dimensional Cauchy-Riemann type systems. Vector- and Clifford algebra-valued Eisenstein and Poincaré series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. In particular, explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series are established and a concept of hypercomplex multiplication of lattices is introduced.
Applications to the theory of Hilbert spaces with reproducing kernels, to partial differential equations and index theory on some conformal manifolds are also described.
Zielgruppe
Graduates, postgraduates and researchers in analysis and number theory, physicists
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
- Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Algebra Zahlentheorie
Weitere Infos & Material
Introduction.- 1. Function Theory in Hypercomplex Spaces.- 2. Clifford-analytic Eisenstein Series Associated to Translation Groups.- 3. Clifford-analytic Modular Forms.- Bibliography.- Index.
