It is known that the Riemann zeta-function \(\zeta (s)\) is universal in the sense that the shifts \(\zeta (s+i\tau )\), \(\tau \in \mathbb {R}\), approximate a wide class of analytic functions. In the paper, the approximation by generalized shifts \(\zeta (s+i\varphi (\tau ))\), where \(\varphi (\tau )\) is a certain differentiable function, is considered, and the property of the density for the above shifts in short intervals is obtained.

中文翻译：

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在短时间间隔内通过黎曼zeta函数的广义位移进行逼近

众所周知，黎曼zeta函数\ {\ zeta（s）\）在以下意义上是通用的，即移位\ {\ zeta（s + i \ tau）\），\（\ tau \ in \ mathbb {R } \），近似分析函数的种类。在本文中，考虑了广义位移\（\ zeta（s + i \ varphi（\ tau））\）的逼近，其中\（\ varphi（\ tau）\）是一个可微的函数，并且其性质在较短的间隔内获得了上述位移的密度。