The lacunary-series tag has no usage guidance.

**11**

votes

**1**answer

402 views

### 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

**1**answer

316 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

**1**answer

173 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 ...