Re: Exposition of Riemann Surfaces

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#155

From: William F. Hammond
Date: Sat, 26 Dec 1992 22:16

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In article <1he1p8INNlh0@mozz.unh.edu> dvf@kepler.unh.edu
(David V Feldman) writes:

> I am wondering if anyone has ever given an exposition of the
> basic theory of Riemann surfaces that systematically did everything
> on the universal covering space.  The idea would be that having
> global coordinates would allow all objects such as differentials
> of various sorts to be viewed as functions with appropriate
> transformation properties,  . . .

This is the theory of "automorphic functions" in dimension 1.
For a first reference I would suggest:  C. L. Siegel, Topics in
Complex Function Theory, volume II (Automorphic Functions and Abelian
Integrals), English translation by A. Shenitzer & M. Tretkoff,
Interscience Tracts in Pure & Appl. Math., No. 25, Wiley-Interscience,
1971.

----------------------------------------------------------------------
William F. Hammond                   Dept. of Mathematics & Statistics
518-442-4625                         SUNYA, Albany, NY 12222 (U.S.A.)
hammond@csc.albany.edu               FAX: 518-442-4731
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From: hammond@csc.albany.edu (William F. Hammond)
Subject: Re: Exposition of Riemann Surfaces
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