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Holomorphic Functions with Prescribed Zeros

  • Reinhold Remmert
Part of the Graduate Texts in Mathematics book series (GTM, volume 172)

Abstract

We extend the results obtained in Chapter 3 for entire functions to functions holomorphic in arbitrary regions D in ℂ. Our goal is to prove that every divisor on D is a principal divisor (existence theorem 1.5). For this purpose we first construct, in Section 1, Weierstrass products for every positive divisor. As before, they are built up from Weierstrass factors E n and converge normally in regions that contain ℂ\∂D (product theorem 1.3). In Section 2 we develop, among other things, the theory of the greatest common divisor for integral domains O(G).

Keywords

Holomorphic Function Blaschke Product Great Common Divisor Product Theorem Normal Convergence 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Reinhold Remmert
    • 1
  1. 1.Mathematisches InstitutWestfälische Wilhelms—Universität MünsterMünsterGermany

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