Siegel's modular forms and dirichlet series : Course given at the University of Maryland, 1969-1970

• Main Author: Maass, Hans
• Format: eBook Book
• Language: English
• Published: Berlin, Heidelberg Springer-Verlag 1971; Springer Berlin / Heidelberg; Springer Berlin Heidelberg; Springer
• Edition: 1
• Series: Lecture Notes in Mathematics
• Subjects: Dirichlet series; Forms, Modular; Mathematics; Mathematics and Statistics; Modular groups; Number Theory; Series, Dirichlet
• ISBN: 3540055630; 9780387055633; 0387055630; 9783540055631; 9783662202487; 3662202484
• ISSN: 0075-8434; 1617-9692
• DOI: 10.1007/BFb0058625

Preliminary remarks on topological groups.- Automorphism groups of bilinear forms.- Geometry in the representation space.- Symplectic geometry.- Weakly symmetric Riemannian spaces.- The Riemannian space of all positive matrices.- A generalization of JS(X).- The Riemannian space.- The reduction theor...

Table of Contents:

• Preliminary remarks on topological groups -- Automorphism groups of bilinear forms -- Geometry in the representation space -- Symplectic geometry -- Weakly symmetric Riemannian spaces -- The Riemannian space of all positive matrices -- A generalization of JS(X) -- The Riemannian space -- The reduction theory of positive quadratic forms -- Größen-characters of quadratic forms -- The modular group of degree n -- The fundamental domain of the modular group -- Modular forms of degree n -- Report on Eisenstein series of the modular group -- Dirichlet series corresponding to modular forms -- Zeta functions attached to quadratic forms -- Selberg's zeta functions -- Non-analytic Eisenstein series -- The differential operaton M? -- Final aspects.