ICTS:30193

Video URL

The problem of representing a non-zero integer by indefinite integral quaternary quadratic forms: t…

The problem of representing a non-zero integer by indefinite integral quaternary quadratic forms: the circle method and beyond

(2024). The problem of representing a non-zero integer by indefinite integral quaternary quadratic forms: the circle method and beyond. SciVideos. https://youtube.com/live/kyx0TK249mA

The problem of representing a non-zero integer by indefinite integral quaternary quadratic forms: the circle method and beyond. SciVideos, Nov. 06, 2024, https://youtube.com/live/kyx0TK249mA 

          @misc{ scivideos_ICTS:30193,
            doi = {},
            url = {https://youtube.com/live/kyx0TK249mA},
            author = {},
            keywords = {},
            language = {en},
            title = {The problem of representing a non-zero integer by indefinite integral quaternary quadratic forms: the circle method and beyond},
            publisher = {},
            year = {2024},
            month = {nov},
            note = {ICTS:30193 see, \url{https://scivideos.org/index.php/icts-tifr/30193}}
          }
Satadal Ganguly
Talk numberICTS:30193
Source RepositoryICTS-TIFR
Source EventCircle Method and Related Topics
Collection

Abstract

I will discuss the problem of obtaining an asymptotic formula for counting integral solutions to an equation of the form f(x, y, z, w)=N in an expanding box, where N is a non-zero integer and f is an indefinite quadratic form over the integers. For forms of the shape axy-bzw, I will then explain how we can obtain a significantly strong error term by applying deep methods from the spectral theory of automorphic forms. This is a joint work with Rachita Guria.