Geodesic
Power series with fast decreasing coefficients
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 167-175 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $f(x)=\sum_{n=0}^\infty a_nx^n$ be an analytic function in the unit disc such that for some $\lambda>1$, $C_0,C_1,C_2,C_3>0$ we have $$ |f(x)|\le C_0\exp(-C_1|\log(1-x)|^\lambda),\qquad\frac12<x<1 $$ and $$|a_n|\le C_2\exp\biggl(-C_3\frac{\sqrt n}{\log(n+2)}\biggr),\qquad n\ge0. $$ Then $f\equiv0$. Bibl. – 5 titles. 
@article{ZNSL_2010_376_a6,
     author = {A. M. Chirikov},
     title = {Power series with fast decreasing coefficients},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {167--175},
     year = {2010},
     volume = {376},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a6/}
}
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A. M. Chirikov. Power series with fast decreasing coefficients. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 167-175. http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a6/

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