Hecke eigenvalues of GL(n) Hecke-Maass forms
Grant Data
Project Title
Hecke eigenvalues of GL(n) Hecke-Maass forms
Principal Investigator
Professor Lau, Yuk Kam
(Principal Investigator (PI))
Duration
36
Start Date
2018-01-01
Amount
472351
Conference Title
Hecke eigenvalues of GL(n) Hecke-Maass forms
Presentation Title
Keywords
Equidistributions, GL(n) automorphic forms, Hecke eigenvalues, Maass forms
Discipline
Pure Mathematics
Panel
Physical Sciences (P)
HKU Project Code
17305617
Grant Type
General Research Fund (GRF)
Funding Year
2017
Status
Completed
Objectives
1 Enhance a method of Matz & Templier so as to derive a close analogue of Sarnak's results toward the Ramanujan conjecture. 2 Derive a result toward the generalized Lang-Trotter conjecture and extend the quantitative equidistribution results in the case of GL(2) to GL(n). 3 Explore the arithmetic properties of the main term in the trace formula for the Hecke eigenvalues over a family of Hecke-Maass forms, such as the condition for a vanishing main term. 4 Explore applications in combinatorics: Develop an effective rule or algorithm for the determination of some Littlewood-Richardson coefficients. 5 Train a graduate student to study in this area.