Density of zeros of the Riemann zeta function in narrow rectangles of the critical strip
https://doi.org/10.22405/2226-8383-2025-26-5-158-183
Abstract
For the number of zeros of the Riemann zeta-function 𝜁(𝑠) in narrow rectangles of the critical
strip (Re 𝑠 ⩾ 𝛼 ⩾ 0.5 and 𝑇 < Im𝑠 ⩽ 𝑇 + 𝐻), assuming
where (𝜅, 𝜆) is an arbitrary exponent pair, 𝜀 < 10^(−4) is any fixed positive number, and
𝑇 ⩾ 𝑇0(𝜀) > 0, an estimate of the form
is obtained. Here 𝑎 = 2, 4 and 𝑐 = 172 when 1/2 ⩽ 𝛼 ⩽ 2/3 or 5/6 ⩽ 𝛼 ⩽ 1, and respectively 𝑎 = 8/3 and 𝑐 = 50 when 2/3 < 𝛼 < 5/6 .
About the Author
Zarullo Khusenovich Rakhmonov
Tajik National University
Tajikistan
Tajikistan
doctor of physical and mathematical sciences, Academician of the National Academy of Sciences of Tajikistan
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Review
For citations:
Rakhmonov Z.Kh. Density of zeros of the Riemann zeta function in narrow rectangles of the critical strip. Chebyshevskii Sbornik. 2025;26(5):158-183. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-5-158-183
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