Geodesic
A theorem on stability of the argument of characteristic function
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 1, pp. 70-79 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $f(x)$ be the characteristic function of a probability distribution on the line. If $1-|f(t)|\le\varepsilon$ for $|t|\le a$ and, moreover, $\varepsilon\le C_1$, then $$ \min_{\beta\in R} \max_{|t|\leq a}|\arg f(t)-\beta t|\leq C_2\varepsilon^{3/4}, $$ where $C_1$, $C_2$ are suitable absolute constants. 
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     author = {A. I. Il'inskii},
     title = {A theorem on stability of the argument of characteristic function},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {70--79},
     year = {1996},
     volume = {3},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a6/}
}
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A. I. Il'inskii. A theorem on stability of the argument of characteristic function. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 1, pp. 70-79. http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a6/