The ball and some Hilbert problems
By: Rolf-Peter Holzapfel.
Series: Lectures in mathematics ETH Zürich
Publisher: Birkhäuser Verlag; Birkhäuser
Published: 1995
Place of publication: Basel; Boston
Language: eng
Number of pages: 160
Subjects: Unit ball.; Picard schemes.; Curves, Elliptic.
Description: The famous twelfth Hilbert problem calls for holomorphic functions in several variables with properties analogous to the exponential function and the elliptic modular function with a view to the explicit construction of (Hilbert) class fields by means of special values. The lecture notes present those functions living on the two-dimensional complex unit ball.

In the course of their construction, the reader is introduced to work with complex multiplication, moduli fields, moduli space of curves, surface uniformizations, Gauss-Manin connection, Jacobian varieties, Torelli's theorem, Picard modular forms, Theta functions, class fields and transcendental values in an effective manner.
Notes: Includes bibliographical references (p. [151]-156) and index.