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 24, 2017 11:30, Moscow, Steklov Mathematical Institute
 


Inverse residues and Pyatetski-Shapiro sequences

M. A. Korolevab

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Video records:
MP4 906.5 Mb
MP4 229.9 Mb

Number of views:
This page:153
Video files:35

M. A. Korolev
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: Let $c>1$ be fixed non-integer. Then the set $\mathcal{P}_{c}$ of integers $m = [n^{c}]$, $n = 1,2,3,\ldots$ is called as Pyatetskii -Shapiro sequence. There are a lot of papers devoted to different number -theoretical problems with the elements of the sequences $\mathcal{P}_{c}$.
In the talk, we will speak about the distribution of inverse residues modulo $q$ for the elements of Pyatetskii -Shapiro sequence, that is, about the distribution of the solution of the congruence
$$ mm^{*} \equiv 1 \pmod q $$
with the conditions $m\in \mathcal{P}_{c}$, $1\leqslant m\leqslant X$, where $X = X(c,q)\to +\infty$ as $q\to +\infty$.

Language: English

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018