Analytic continuation and fixed points of the Poincaré mapping for a polynomial Abel equation

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...

Analytic continuation, functional equation: examples

1. L(s, χ) for even Dirichlet characters 2. L(s, χ) for odd Dirichlet characters 3. Dedekind zeta function ζ o (s) for Gaussian integers o 4. Grossencharacter L-functions L-functions for Gaussian integers We try to imitate the argument used by Riemann for proving the analytic continuation of ζ(s) and its functional equation π −s/2 Γ(s 2) ζ(s) = π −(1−s)/2 Γ(1−s 2) ζ(1 − s) from the integral rep...

Analytic Continuation in Mapping Spaces

We consider a Stein manifold M of dimension ≥ 2 and a compact subset K ⊂ M such that M ′ = M\K is connected. Let S be a compact differential manifold, and let MS , resp. M ′ S stand for the complex manifold of maps S → M , resp. S → M , of some specified regularity that are homotopic to constant. We prove that any holomorphic function on M ′ S continues analytically to MS (perhaps as a multival...

Fixed Points of Analytic Functions

An Analytic Algorithm for Generalized Abel Integral Equation

In this paper, a homotopy perturbation method (HPM) and modified homotopy perturbation (MHPM) are proposed to solve singular integral equation with generalized Abel's kernel.