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Computing the Schottky-Klein Prime Function on the Schottky Double of Planar Domains

Computing the Schottky-Klein Prime Function on the Schottky Double of Planar Domains A numerical algorithm is presented for the computation of the Schottky-Klein prime function on the Schottky double of multiply connected circular domains in the plane. While there exist classical formulae for the Schottky-Klein prime function in the form of infinite products over a Schottky group, such products are not convergent for all choices of multiply connected circular domains. The prime function itself, however, is a well-defined function for any multiply connected circular domain. The present algorithm facilitates the evaluation of this prime function when the planar domains are such that the classical infinite product representation is either not convergent or so slowly convergent as to be impracticable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Computing the Schottky-Klein Prime Function on the Schottky Double of Planar Domains

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Publisher
Springer Journals
Copyright
Copyright © 2007 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321646
Publisher site
See Article on Publisher Site

Abstract

A numerical algorithm is presented for the computation of the Schottky-Klein prime function on the Schottky double of multiply connected circular domains in the plane. While there exist classical formulae for the Schottky-Klein prime function in the form of infinite products over a Schottky group, such products are not convergent for all choices of multiply connected circular domains. The prime function itself, however, is a well-defined function for any multiply connected circular domain. The present algorithm facilitates the evaluation of this prime function when the planar domains are such that the classical infinite product representation is either not convergent or so slowly convergent as to be impracticable.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jan 19, 2007

References