Number Theory pp 211-214 | Cite as

A Gap Theorem for Differentially Algebraic Power Series

  • Leonard Lipshitz
  • Lee A. Rubel
Conference paper


One of the ways to force an analytic function to be pathological is to suppose that its power series has large gaps. If \( f(z) = \sum\limits_{k = 0}^\infty {f{k^{{z^k}}}} \) is a formal power series, we define the spectrum of f by σ(f) = {k : f k ≠ 0}. It is possible to gain information about the analytical behaviour of f from the knowledge of σ(f) alone.


Power Series Analytical Behaviour Theta Function Formal Power Series Recursion Formula 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Leonard Lipshitz
    • 1
  • Lee A. Rubel
    • 2
  1. 1.Purdue UniversityIndianapolisUSA
  2. 2.University of IllinoisUrbanaUSA

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