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aequationes mathematicae

, Volume 54, Issue 1–2, pp 87–101 | Cite as

On factorizing meromorphic functions

  • Ian N. Baker
Research Papers

Summary

The paper determines all cases when a meromorphic functionF can be expressed both asfp andfq with the same meromorphicf and different polynomialsp andq. In all cases there are constantsk, β, a positive integerm, a root λ of unity of orderS and a polynomialr such thatp=(Lr) m+k,q=r m+k, whereLz=λz+β. We have eitherm=1,S arbitrary orm=2,S=2, which can occur even ifF andf are entire, or, in the remaining casesS=2, 3, 4 or 6,m dividesS andf(k+t m) is a doubly-periodic function.

AMS (1991) subject classification

Primary 30D05 Secondary 30D35 39B12 58F08 

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Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Ian N. Baker
    • 1
  1. 1.Department of MathematicsImperial CollegeLondonEngland

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