Automorphic functions and Abelian integrals
Author(s)
Bibliographic Information
Automorphic functions and Abelian integrals
（Wiley classics library, . Topics in complex function theory / by C.L. Siegel ; v. 2）
Wiley-Interscience, 1988, c1971
Wiley classics library ed
- : pbk
- Other Title
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Automorphic and abelian integrals
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Note
Includes cumulative index vols. 1 and 2
2nd of three parts corresponding to three consecutive courses taught by Carl L. Siegel at the Univesity of Göttingen. Lecture notes, in German, were taken by Erhard Gottschling and (for second half of Part III) by Helmut Klingen
Description and Table of Contents
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.
Table of Contents
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
by "Nielsen BookData"