Kloosterman sums and Hurwitz class numbers
Grant Data
Project Title
Kloosterman sums and Hurwitz class numbers
Principal Investigator
Professor Lau, Yuk Kam
(Principal Investigator (PI))
Duration
36
Start Date
2020-01-01
Completion Date
2024-01-11
Amount
502444
Conference Title
Kloosterman sums and Hurwitz class numbers
Keywords
Equidistribution, Hurwitz class numbers, Kloosterman sums, Mock modular forms
Discipline
Pure Mathematics
Panel
Physical Sciences (P)
HKU Project Code
17303619
Grant Type
General Research Fund (GRF)
Funding Year
2019
Status
Completed
Objectives
1 Investigate the statistical properties of Kloosterman sums over function fields on a thin set (short interval). The task is to confirm the distribution and to estimate the rate of convergence with an attempt to evaluate explicitly possible secondary terms. 2 Explore the connections between Hurwitz class numbers and Kloosterman sums. The primary goal is to evaluate (asymptotic results for) a specific weighted sum of Hurwitz class numbers over an arithmetic progression. 3 Understand the underlying modularity the Hurwitz class numbers, such as the specific sum in Objective 2, using the theories of modular forms and mock modular forms. 4 Train a graduate student to work in this area.