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Entire Functions with Prescribed Zeros

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

Abstract

If f ≠ 0 is a holomorphic function on a domain G,its zero set Z(f) is locally finite in G by the identity theorem (cf. I.8.1.3). It is natural to pose the following problem:

Let T be any locally finite subset of G, and let every point d ∈ T be assigned a natural number ∂(d) ≥ 1 in some way. Construct functions holomorphic in G which each have zero set T and, moreover, whose zeros at each point d E T have order ∂(d).

Keywords

Holomorphic Function Entire Function Meromorphic Function Elliptic Function Product Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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