Number Theory Seminar: Arithmetic properties of weakly holomorphic modular functions of arbitrary level
- Event Type
- Seminar/Symposium
- Sponsor
- n/a
- Location
- 241 Altgeld Hall
- Date
- Sep 21, 2021 11:00 am
- Speaker
- Soon-Yi Kang, Kangwon National University, Korea
- Contact
- Bruce Berndt
- berndt@illinois.edu
- Views
- 17
Abstract: The canonical basis of the space of modular functions on the modular group of genus zero form a Hecke system. From this fact, many important properties of modular functions were derived. Recently, we have proved that the Niebur-Poincare basis of the space of Harmonic Maass functions also forms a Hecke system. In this talk, we show its applications, including divisibility of Fourier coefficients of modular functions of arbitrary level, higher genus replicability, and values of modular functions on divisors of modular forms.