Number Theory pp 211-214 | Cite as

A Gap Theorem for Differentially Algebraic Power Series

  • Leonard Lipshitz
  • Lee A. Rubel
Conference paper

Zusammenfassung

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.

Keywords

Power Series Analytical Behaviour Theta Function Formal Power Series Recursion Formula 
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 1991

Authors and Affiliations

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

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