Email this article On square of the Riemann zeta function modulus in the critical strip and estimates of means
- Authors: Zobnin A.V.1
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Affiliations:
- Joint Institute for High Temperatures of the Russian Academy of Sciences, Moscow, Russia
- Issue: Vol 216, No 4 (2025)
- Pages: 35-43
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/306695
- DOI: https://doi.org/10.4213/sm10113
- ID: 306695
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Abstract
A new integral representation is derived for the square of the modulus of the Riemann zeta function. Estimates of the Laplace transform of the residual term $E_\sigma(T)$ and of the mean value with respect to a Gaussian function of the square of the modulus of the zeta function are obtained.Bibliography: 6 titles.
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About the authors
Andrey Vyacheslavovich Zobnin
Joint Institute for High Temperatures of the Russian Academy of Sciences, Moscow, Russia
Author for correspondence.
Email: zobnin@ihed.ras.ru
Doctor of physico-mathematical sciences, Senior Researcher
References
- A. Ivic, Lectures on mean values of the Riemann zeta function, Tata Inst. Fund. Res. Lectures on Math. and Phys., 82, Springer-Verlag, Berlin, 1991, viii+363 pp.
- A. Ivic, K. Matsumoto, “On the error term in the mean square formula for the Riemann zeta-function in the critical strip”, Monatsh. Math., 121:3 (1996), 213–229
- В. А. Кухта, “О среднем значении модуля дзета-функции Римана в критической полосе”, Вестн. Моск. ун-та. Сер. 1. Матем., мех., 2010, № 5, 64–67
- А. Лауринчикас, “Оценка роста преобразования Меллина дзета-функции Римана”, Матем. заметки, 89:1 (2011), 70–81
- Е. К. Титчмарш, Теория дзета-функции Римана, ИЛ, М., 1953, 409 с.
- E. Hecke, “Über analytische Funktionen und die Verteilung von Zahlen mod. eins”, Abh. Math. Sem. Univ. Hamburg, 1:1 (1922), 54–76
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