A study on the Fourier coefficients of cusp forms of half-integral weight

Professor Lau, Yuk Kam   (Principal Investigator (PI))

42

2017-01-01

488501

A study on the Fourier coefficients of cusp forms of half-integral weight

Arithmetic functions, Asymptotic results, Dirichlet series, Forms of half-integral weight, Rankin-Selberg L-functions

Pure Mathematics

Physical Sciences (P)

17313616

General Research Fund (GRF)

2016

Completed

1 Develop a new robust tool for the local weighted mean with an application to the gap width between sign-changes for coefficients of automorphic L-functions, L-functions in the extended Selberg class (which may have no Euler products). 2 Enlarge the known region of holomorphicity of the Dirichlet series associated to the Fourier coefficients supported on squarefree integers 3 Study the Dirichlet series of Rankin-Selberg convolution of the Fourier coefficients over squarefree numbers 4 Study heuristically the plausibility of a conjecture on the mean value of order of some Tate-Shafarevich groups and investigate the asymptotic behaviour of the mean value of these orders with mollifying factors. 5 Train graduate student(s), M.Phil or Ph.D, to work in this area.