A Gap Theorem for Differentially Algebraic Power Series

Leonard Lipshitz and Lee A. Rubel
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Leonard Lipshitz: Purdue University
Lee A. Rubel: University of Illinois

Chapter 10 in Number Theory, 1991, pp 211-214 from Springer

Abstract: 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 ) = ∑ k = 0 ∞ f k z k $$ f(z) = \sum\limits_{k = 0}^\infty {f{k^{{z^k}}}} $$ 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 (search for similar items in EconPapers)
Date: 1991
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DOI: 10.1007/978-1-4757-4158-2_10

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