Geodesic
On a Class of Sine-Type Functions
Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 941-954

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We study an infinite product $F_\Lambda(z)$ with zeros $\lambda_n=n+l(|n|)$, $n\in\mathbb Z$, where $l(t)$ is a concave function and $l(t)=o(t)$. We obtain a test for $F_\Lambda(z)$ to belong to the class of sine-type functions. For the particular case in which $l(t)$ is a regularly varying function, we obtain sharp asymptotic estimates for $F_\Lambda(z)$.
Keywords: sine-type function, concave function, regularly varying function, hypergeometric function, Riesz basis, analytic function. 
@article{MZM_2008_83_6_a12,
     author = {A. A. Yukhimenko},
     title = {On a {Class} of {Sine-Type} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {941--954},
     publisher = {mathdoc},
     volume = {83},
     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a12/}
}
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A. A. Yukhimenko. On a Class of Sine-Type Functions. Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 941-954. http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a12/