The ball and some Hilbert problems
by Rolf-Peter Holzapfel
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.
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The ball and some Hilbert problems
1995, Birkhäuser Verlag, Birkhäuser
in English
3764328355 9783764328351
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Includes bibliographical references (p. [151]-156) and index.
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