Geodesic
On real zeros of the derivative of the Hardy function
Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 234-240

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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. 
Sh. A. Khayrulloev. On real zeros of the derivative of the Hardy function. Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 234-240. http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a14/
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