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Topics in Complex Function Theory, Volume 2: Automorphic Functions and Abelian Integrals

Topics in Complex Function Theory, Volume 2: Automorphic Functions and Abelian Integrals

Carl Ludwig Siegel

ISBN: 978-0-471-60843-1

Feb 1988

208 pages

Select type: Paperback

In Stock

$211.00

Description

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