On Convergence Sets of Formal Power Series

Daowei Ma; Tejinder S. Neelon

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arXiv · 1205.2577

On Convergence Sets of Formal Power Series

Daowei Ma·Tejinder S. Neelon

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Abstract

The (projective) convergence set of a divergent formal power series $f(x_{1},...,x_{n})$ is defined to be the image in $\PP^{n-1}$ of the set of all $x\in \mathbb{C}^{n}$ such that $f(x_{1}t,...,x_{n}t)$, as a series in $t$, converges absolutely near $t=0$. We prove that every countable union of closed complete pluripolar sets in $\PP^{n-1}$ is the convergence set of some divergent series $f$. The (affine) convergence sets of formal power series with polynomial coefficients are also studied. The higher-dimensional results of A. Sathaye, P. Lelong, N. Levenberg and R.E. Molzon, and of J. Ribón are thus generalized.

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BibTeX RIS

Daowei Ma, Tejinder S. Neelon. 2012-05-23. On Convergence Sets of Formal Power Series. https://arxiv.org/abs/1205.2577

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