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10
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1answer
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Distribution of zeroes of lacunary functions

In a recent Math Stack Exchange question I asked about the function $$f(z)=\sum_{n=0}^\infty z^{2^n},$$ and was informed of its status is a canonical example of a lacunary series with natural boundary ...
1
vote
1answer
225 views

Lacunary sequence

Is there a standard definition for a lacunary sequence? Suppose $0 < a_1 < a_2 < \cdots.$ I've read two papers using the term recently. One requires $$ \liminf_n\frac{a_{n+1}}{a_n}>1 $$ ...
2
votes
1answer
163 views

Coefficients of lacunary series on quasiconformally transformed unit disk

Say I have a lacunary $q$ series $s(q)=\sum_{n=0}^{\infty} a_{n}q^{n}$ , and I have a quasiconformal transformation $\xi$ which preserves the boundary of the unit disk in $\mathbb{C}$ such that if ...