ICTS:30201

Video URL

Second moment of the GL_3 standard L-function on the critical line. (Online)

Second moment of the GL_3 standard L-function on the critical line. (Online)

(2024). Second moment of the GL_3 standard L-function on the critical line. (Online). SciVideos. https://youtube.com/live/TcoZ4CITCAk

Second moment of the GL_3 standard L-function on the critical line. (Online). SciVideos, Nov. 07, 2024, https://youtube.com/live/TcoZ4CITCAk 

          @misc{ scivideos_ICTS:30201,
            doi = {},
            url = {https://youtube.com/live/TcoZ4CITCAk},
            author = {},
            keywords = {},
            language = {en},
            title = {Second moment of the GL_3 standard L-function on the critical line. (Online)},
            publisher = {},
            year = {2024},
            month = {nov},
            note = {ICTS:30201 see, \url{https://scivideos.org/icts-tifr/30201}}
          }
Mathew P. Young
Talk numberICTS:30201
Source RepositoryICTS-TIFR
Source EventCircle Method and Related Topics
Collection

Abstract

The second and fourth moments of the Riemann zeta function have been known for about a century, but the sixth moment remains elusive. The sixth moment of zeta can be thought of as the second moment of a GL_3 Eisenstein series, and it is natural to consider variants of the problem where the Eisenstein series is replaced by a cusp form. I will discuss recent work with Agniva Dasgupta and Wing Hong Leung where we obtain a nontrivial bound on this second moment. I will also discuss some applications, including an improvement on the Rankin-Selberg problem.