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On real zeros of the derivative of the Hardy function
Sh. A. Khayrulloev Tajik National University (Dushanbe)
Abstract:
The existence of the zeros of the Riemann zeta-function in the short segments of the critical line (or the real zeros of Hardy's function $Z(t)$, that is the same) is one of the topical problems in the theory of the Riemann zeta-function. The study of the zeros of Hardy function's derivatives $Z^{(j)}(t)$ is the generalization of such problem. Let $T>0$. Let us define the quantity $H_j(T)$, the distance from $T$ to the nearest real zero not less than $T$ of the $j$-th derivative of the Hardy function. In the paper, an upper bound for $H_j(T)$ is proved.
Keywords:
Hardy function, Riemann zeta function, exponential pair, trigonometric sum, critical line, odd order zero.
Received: 28.05.2021 Accepted: 21.12.2021
Citation:
Sh. A. Khayrulloev, “On real zeros of the derivative of the Hardy function”, Chebyshevskii Sb., 22:5 (2021), 234–240
Linking options:
https://www.mathnet.ru/eng/cheb1129 https://www.mathnet.ru/eng/cheb/v22/i5/p234
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Abstract page: | 67 | Full-text PDF : | 15 | References: | 10 |
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