On real zeros of the derivative of the Hardy function
https://doi.org/10.22405/2226-8383-2021-22-5-234-240
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.
About the Author
Shamsullo Amrulloevich Khayrulloev
Tajik National University
Tajikistan
Tajikistan
candidate of physical and mathematical sciences
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Review
For citations:
Khayrulloev Sh.A. On real zeros of the derivative of the Hardy function. Chebyshevskii Sbornik. 2021;22(5):234-240. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-5-234-240
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