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I am worinkg with the complex function $\sum_{n=0}^\infty z^{3^n}$ . How can I prove that the function cannot be analytically continued past the unit circle.

Any help is welcome!

Almhz
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    show that the series is infinite at all roots of unity of order various powers of three and show that those are dense in the unit circle; conclude – Conrad May 10 '20 at 01:18
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    $f(z)=z+f(z^{3})$. Use the argument in the following link: https://math.stackexchange.com/questions/264413/analytic-continuation-of-a-power-series-2?rq=1 – Kavi Rama Murthy May 10 '20 at 05:18
  • I´ll try the argument! Thanks. – Almhz May 10 '20 at 19:14

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