Geodesic
Canonical products generated by perturbations of the sequence of integers, and their asymptotic estimation
Izvestiya. Mathematics , Tome 74 (2010) no. 5, pp. 1083-1101

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We obtain asymptotic estimates for canonical products with complex zeros of the form $\lambda_n=n+o(n)$. A formula is found for the excess of the system of exponentials $\{e^{i\lambda_nt}\}_{n\in\mathbb{Z}}$ in the space $L^2(-\pi,\pi)$. We consider some particular cases of sequences $\{\lambda_n\}_{n\in\mathbb{Z}}$.
Keywords: canonical product, asymptotic estimate, slowly varying function, excess of a system. 
@article{IM2_2010_74_5_a6,
     author = {A. A. Yukhimenko},
     title = {Canonical products generated by perturbations of the sequence of integers, and their asymptotic estimation},
     journal = {Izvestiya. Mathematics },
     pages = {1083--1101},
     publisher = {mathdoc},
     volume = {74},
     number = {5},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2010_74_5_a6/}
}
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A. A. Yukhimenko. Canonical products generated by perturbations of the sequence of integers, and their asymptotic estimation. Izvestiya. Mathematics , Tome 74 (2010) no. 5, pp. 1083-1101. http://geodesic.mathdoc.fr/item/IM2_2010_74_5_a6/