Entire Functions with Prescribed Zeros

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


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).


Holomorphic Function Entire Function Meromorphic Function Elliptic Function Product Theorem 
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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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