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科学研究
RESEARCH
Hecke system of harmonic Maass functions and applications to modular curves of higher genera
时间  Datetime
2021-01-28 16:00 — 17:00
地点  Venue
Zoom APP()
报告人  Speaker
Chang Heon Kim
单位  Affiliation
SKKU
邀请人  Host
费佳睿
备注  remarks
ID:95549212478, password: 120205
报告摘要  Abstract

The unique basis functions $j_m$ of the form $q^{-m}+O(q)$ for the space of weakly holomorphic modular functions on the full modular group form a Hecke system. This feature was a critical ingredient in proofs of arithmetic properties of Fourier coefficients of modular functions and denominator formula for the Monster Lie algebra.


In this talk, we consider the basis functions of the space of harmonic weak Maass functions of an arbitrary level, which generalize $j_m$, and show that they form a Hecke system as well. As applications, we establish some divisibility properties of Fourier coefficients of weakly holomorphic modular forms on modular curves of genus $\ge1$. Furthermore, we present a general duality relation that these modular formssatisfy.
This is a joint work with Daeyeol Jeon and Soon-Yi Kang.