The paper is a continuation of Korolev and Laurinčikas (Aequ Math 93:859–873, 2019), where theorems on the approximation of analytic functions by shifts \(\zeta (s+iht_k)\), \(h>0\), \(k\in {\mathbb {N}}\), and \(t_k\) are the Gram points, were obtained. In this paper, it is proved, that the set of shifts \(\zeta (s+iht_k)\) has a positive density in short intervals \([N, N+M]\) with \(M=o(N)\).

中文翻译：

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Gram点的新应用。II

本文是Korolev和Laurinčikas（Aequ Math 93：859–873，2019）的延续，其中关于通过移位\（\ zeta（s + iht_k）\），\（h> 0 \）逼近解析函数的定理，\（k \ in {\ mathbb {N}} \）和\（t_k \）是Gram点。在本文中，证明了偏移集\（\ zeta（s + iht_k）\）在短间隔\（[N，N + M] \）中具有\（M = o（N ）\）。