Applications of the Circle Method to Multiplicative Number Theory

Lead Research Organisation: University of Warwick
Department Name: Mathematics

Abstract

The circle method is a tool from harmonic analysis that has traditionally been applied to investigate additive number theory problems, such as Waring's problem about writing numbers as a sum of k-th powers. As well as continuing exciting developments in those applications, the circle method can also be used to investigate some multiplicative number theory problems that would traditionally be studied using other tools like Dirichlet L-functions. this PhD thesis will pursue new research in these directions. A starting problem is to investigate the variance of general sequences in arithmetic progressions using the circle method, building on recent work of Harper and Soundarajan for certain special sequences. It is intended that the thesis will move on to look at developments such as Heflgott's complete resolution of the ternary Goldbach conjecture via the circle methods, seeking to streamline and strengthen his argument in various ways. This all fits in to EPSRC's number theory research area.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R513374/1 01/10/2018 30/09/2023
2104215 Studentship EP/R513374/1 01/10/2018 31/03/2022 Daniele Mastrostefano