Asymptotic behaviour of even canonical products with slight abnormalities in the distribution of the set of zeros, which has positive density

The asymptotic behaviour of even canonical products with zeros on the real axis is considered. It is assumed that the set of zeros has density (the sequence $\pm \lambda_{n}$ has density). Sharp asymptotic estimates for the logarithm of the modulus of the canonical product are obtained under certain restrictions on the rate of convergence of the ratio $n/\lambda_{n}$ to its limit.
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