?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
Extra Form
일정시작 2021-04-16
배경색상 #FF5733

Date: 16 Apr. (Fri) 15:00 ~ 16:30

Place: Zoom

Speaker : 김창헌 (성균관대학교)

Title : Hecke system of harmonic Maass functions and applications to modular curves of higher genera

 

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 fo 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 $\geq 1$. Furthemore, we present a general duality relation that these modular forms satisfy. This is a joint work with Daeyeol Jeon and Soon-Yi Kang.

 

 

 


List of Articles
번호 제목 글쓴이 날짜 조회 수
공지 QSMS Mailing List Registration qsms 2021.09.09 13288
30 [Seminar 2021.05.11] Knotted embeddings qsms 2021.05.06 3828
29 [Seminar 2021.05.06] Arithmetic properties of weakly holomorphic modular functions of arbitrary level qsms 2021.05.04 3958
28 [2021 KMS Spring Meeting] Related talks qsms 2021.04.30 7770
» [Seminar 2021.04.16] Hecke system of harmonic Maass functions and applications to modular curves of higher genera qsms 2021.04.19 8601
26 [Seminar 2021.04.02] CM congruence and the derivatives of p-adic L-functions for imaginary quadratic fields qsms 2021.04.19 4912
25 [Seminar 05.14, 05.21, 05.28, 06.04] Introduction to derived categories qsms 2021.04.16 19566
24 [Seminar 2021.04.23] Quiver Hecke algebras and unipotent quantum coordinate ring qsms 2021.04.09 4692
23 [Seminar 2021.04.29] A realization of type A finite $W$-(super)algebra in terms of (super) Yangian qsms 2021.04.09 5425
22 [Seminar 2021.04.02] Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types qsms 2021.03.30 10864
21 [QSMS Monthly Seminar] A survey on symplectic fillings and Milnor fibers of a normal complex surface singularity qsms 2021.03.26 4141
20 [Seminar 2021.03.19] Introduction to zeta functions of groups and rings qsms 2021.03.04 4402
19 [Seminar 2021.03.03] Zeta함수와 L함수에 대한 역사적 고찰X qsms 2021.03.02 12018
18 [Seminar 2021.02.25] Zeta함수와 L함수에 대한 역사적 고찰IX qsms 2021.02.22 4197
17 [Seminar 2021.01.21] Zeta함수와 L함수에 대한 역사적 고찰VIII qsms 2021.01.18 4111
16 [QSMS Monthly Seminiar] Symplectic homology and the McKay correspondence qsms 2021.01.11 4204
15 [Seminar 2021.01.07] Zeta함수와 L함수에 대한 역사적 고찰VII qsms 2021.01.04 3867
14 [Seminar 2020.12.29] Zeta함수와 L함수에 대한 역사적 고찰VI qsms 2020.12.28 3908
13 [Seminar 2020.12.23] Zeta함수와 L함수에 대한 역사적 고찰V qsms 2020.12.21 3938
12 [Seminar 2020.12.17] Zeta함수와 L함수에 대한 역사적 고찰IV qsms 2020.12.08 3665
11 [Seminar 2020.12.10] Zeta함수와 L함수에 대한 역사적 고찰III qsms 2020.12.08 3841
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8