Geodesic
Distribution of roots of quasianalytic functions
Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 3-14

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For functions of certain quasianalytic classes $C\{m_n\}$ on $(-\infty,\infty)$ we determine a function $\xi(x)$, depending on $\{m_n\}$, which is such that a sequence $\{x_k\}$ is a sequence of the roots of $f(x)\in C\{m_n\}$ if and only if for some $a$ $$ \int_a^\infty\frac{dn(x)}{\xi(x - a)}\infty, $$ where $n(x)$ is a distribution function of the sequence $\{x_k\}$. 
@article{MZM_1974_16_1_a0,
     author = {V. S. Konyukhovskii},
     title = {Distribution of roots of quasianalytic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a0/}
}
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V. S. Konyukhovskii. Distribution of roots of quasianalytic functions. Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a0/