Report title: The average size of Ramanujan sums over quadratic number fields

Reporter: Professor Wenguang Zhai ，China University of Mining and Technology

Report time: November 26, 2020 9:00-11:00

Report location: Tencent meeting

Meeting time: 2020/11/26 9:00-11:00

Click the link to join the conference, or add to the conference list:

https://meeting.tencent.com/s/V4VKk0ME8ANa

Conference ID: 532 499 188

One-key dialing to join a conference

+8675536550000,,532499188# (Mainland China)

+85230018898,,,2,532499188# (Hong Kong, China)

Dial based on your location

+8675536550000 ext (Mainland China)

+85230018898 ext (Hong Kong, China)

School contact: Ma Jing jma@jlu.edu.cn

Report summary:

   The Ramanujan sum is an important object in number theory. In this talk, I will give some average results about Ramanujan sums

defined over an arbitrary quadratic number field.

Brief introduction of the speaker:

     Zhai Wenguang, professor and doctoral supervisor of China University of Mining and Technology (Beijing). His research field is analytic number theory. He is currently an editorial board member of journals such as Progress in Mathematics and Pure Mathematics and Applied Mathematics. He has presided over the completion of a number of national and provincial scientific research projects, and published more than 100 academic papers, proving that analytic number theory is in Many important results, such as the use of a unified method to prove the asymptotic formula of the 3rd to 9th integral mean of the remainder of the Dirichlet divisor problem. The method is widely used in the integral mean of a large class of remainders in analytic number theory; analytic number theory is used. Instead of the spectral theory method, the integral mean value and sign change of the remainder of the Weyl law of the Laplace operator eigenvalue on the Heisenberg manifold are studied.