RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
Video Library
Archive
Most viewed videos

Search
RSS
New in collection





You may need the following programs to see the files






А.A.Karatsuba's 80th Birthday Conference in Number Theory and Applications
May 22, 2017 12:15, Moscow, Steklov Mathematical Institute
 


Omega-theorems for Riemann's zeta function and its derivatives near the line $\operatorname{Re}s=1$

A. B. Kalmynin

Department of Mathematics, National Research University "Higher School of Economics"
Video records:
MP4 550.7 Mb
MP4 139.8 Mb

Number of views:
This page:167
Video files:54

A. B. Kalmynin
Photo Gallery


Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: Theorem of Zaitsev [1] states that
$$ \limsup_{s \in \Sigma(T),\;T\to +\infty}\frac{|\zeta(s)|}{\ln T}\geqslant1, $$
where $\Sigma(T)$ denotes the domain
$$ \quad 1-(4+\varepsilon)\frac{\ln\ln\ln t}{\ln\ln t}\leqslant \sigma \leqslant 1,\quad t_{0}<|t|\leqslant T. $$
In this talk, we will present a generalization of Zaitsev's method that allows us to obtain a family of omega-theorems for the Riemann's zeta function and its derivatives in various domains of the critical strip. In particular, we were able to prove that in the same domain $\Sigma(T)$ for all $n$ and arbitrary positive $\delta$ the inequality
$$ \limsup_{s \in \Sigma(T),\;T\to +\infty} \frac{|\zeta^{(n)}(s)|}{e^{(\ln\ln T)^{1+\varepsilon/2-\delta}}}\geqslant1, $$
holds.

Language: English

References
  1. S.P. Zaitsev, “Omega-teorema dlya dzeta-funktsii Rimana vblizi pryamoi $\operatorname{Re}s=1$”, Vestnik Moskovskogo un-ta. Ser. 1. Matematika. Mekhanika, 2000, № 3, 54–57; S.P. Zaitsev, “Omega-theorems for the Riemann zeta-function near the line $\operatorname{Re}s=1$”, Mosc. Univ. Math. Bulletin, 55:3 (2000)  mathscinet  zmath


SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017