Analytic continuation of biholomorphic maps.

Analytic Continuation of a Biholomorphic Mapping

0. Introduction and Preliminary 2 0.1. Existence and uniqueness theorem 2 0.2. Equation of a chain 7 1. Nonsingular matrices 9 1.1. A family of nonsingular matrices 9 1.2. Sufficient condition for Nonsingularity 12 1.3. Estimates 16 2. Local automorphism group of a real hypersurface 23 2.1. Polynomial Identities 23 2.2. Injectivity of a Linear Mapping 33 2.3. Beloshapka-Loboda Theorem 42 3. Com...

5 Extremal Discs and Analytic Continuation of Product Cr Maps

Biholomorphic Maps between Teichmüller Spaces

In this paper we study biholomorphic maps between Teichmüller spaces and the induced linear isometries between the corresponding tangent spaces. The first main result in this paper is the following classification theorem. If M and N are two Riemann surfaces that are not of exceptional type, and if there exists a biholomorphic map between the corresponding Teichmüller spaces Teich(M) and Teich(N...

On Effective Analytic Continuation

Until now, the area of symbolic computation has mainly focused on the manipulation of algebraic expressions. It would be interesting to apply a similar spirit of “exact computations” to the field of mathematical analysis. One important step for such a project is the ability to compute with computable complex numbers and computable analytic functions. Such computations include effective analytic...

Analytic continuation of multiple polylogarithms

It is not hard to see that this function can be analytically continued to a multi-valued memomorhpic function on C. When n > 1 the special value Lin(1) is nothing else but the Riemann zeta value ζ(n), which has great importance in number theory. In recent years, there has been revival of interest in multi-valued classical polylogarithms and their single-valued cousins. For any positive integers...