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






Conference in memory of A. A. Karatsuba on number theory and applications
January 31, 2014 15:40–15:55, Moscow, Steklov Mathematical Institute, Lecture Room 530
 


Additive problems with the summands of a special type

D. V. Goryashin
Video records:
Flash Video 155.4 Mb
Flash Video 930.7 Mb
MP4 155.4 Mb

Number of views:
This page:159
Video files:48

D. V. Goryashin


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: The talk is devoted to the following additive problem. Suppose that $\alpha>1$ is a fixed irrational number. Let $r_3(\alpha,N)$ equals to the number of partitions of $N$ into a sum of two square -free summands and the term of the type $[\alpha q]$ with square -free $q$. In other words, $r_3(\alpha,N)$ is the number of representation $q_1+q_2+[\alpha q_3]=N$ where the numbers $q_1,q_2,q_3$ are square -free. Then the following asymptotic formula holds
$$ r_{3}(\alpha,N) = \frac{1}{2\alpha}(\frac{6}{\pi^2})^{3}N^{2}+O(N^{11/6+\varepsilon}) $$
as $N\to\infty$.

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