Topics in Complex Function Theory, Volume 2

Develops the higher parts of function theory in a unified presentation. Starts with elliptic integrals and functions and uniformization theory, continues with automorphic functions and the theory of abelian integrals and ends with the theory of abelian functions and modular functions in several variables. The last topic originates with the author and appears here for the first time in book form. AUTOMORPHIC FUNCTIONS.

Fractional Linear Transformations.

Noneuclidean Geometry.

Discontinuous Groups.

Polygon Groups.

Poincar Series.

The Field of Automorphic Functions.

Automorphic and Algebraic Functions.

Algebraic Curves of Genus 0 and 1, Canonical Polygons.

ABELIAN INTEGRALS.

Reduction, Existence.

The Period Matrix.

The Modular Group.

Canonical Transformation.

The Theorem of Riemann and Roch.

The Theorem of Abel.

The Jacobi Inversion Problem.

Theta Functions.

The Zeros of the Theta Function.

Theta Quotients.

Jacobi-Abel Functions.

Cumulative Index: Vols.

I & II

Carl Ludwig Siegel was born on December 31, 1896 in Berlin. He studied mathematics and astronomy in Berlin and Gttingen and held chairs at the Universities of Frankfurt and Gttingen before moving to the Institute for Advanced Study in Princeton in 1940. He returned to Gttingen in 1951 and died there in 1981.
Siegel was one of the leading mathematicians of the twentieth century, whose work, noted for its depth as well as breadth, ranged over many different fields such as number theory from the analytic, algebraic and geometrical points of view, automorphic functions of several complex variables, symplectic geometry, celestial mechanics.