?

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 4506
125 [QSMS Monthly Seminar] A survey on symplectic fillings and Milnor fibers of a normal complex surface singularity qsms 2021.03.26 2062
124 [Seminar 2021.04.02] Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types qsms 2021.03.30 8618
123 [Seminar 2021.04.29] A realization of type A finite $W$-(super)algebra in terms of (super) Yangian qsms 2021.04.09 3025
122 [Seminar 2021.04.23] Quiver Hecke algebras and unipotent quantum coordinate ring qsms 2021.04.09 2286
121 [Seminar 05.14, 05.21, 05.28, 06.04] Introduction to derived categories qsms 2021.04.16 17137
120 [Seminar 2021.04.02] CM congruence and the derivatives of p-adic L-functions for imaginary quadratic fields qsms 2021.04.19 2471
» [Seminar 2021.04.16] Hecke system of harmonic Maass functions and applications to modular curves of higher genera qsms 2021.04.19 6174
118 [2021 KMS Spring Meeting] Related talks qsms 2021.04.30 5373
117 [Seminar 2021.05.06] Arithmetic properties of weakly holomorphic modular functions of arbitrary level qsms 2021.05.04 1931
116 [Seminar 2021.05.11] Knotted embeddings qsms 2021.05.06 1767
115 [Seminar 2021.05.12] Equivariant symplectic homology qsms 2021.05.06 1704
114 [QSMS Monthly Seminar] Recoverable lattices qsms 2021.05.07 1594
113 [Seminar 2021.05.14] On some results about non-holomorphic Jacobi forms qsms 2021.05.11 1831
112 [Seminar 2021.05.13] Convergence of harmonic maps via regular nodes qsms 2021.05.12 1784
111 [Seminar 2021.05.18] The coherent-constructible correspondence for toric projective bundles qsms 2021.05.17 1859
110 [Seminar 2021.05.28] Ramanujan continued fractions of order sixteen qsms 2021.05.21 2504
109 [Seminar 2021.06.15, 06.22] Cluster algebras with a view toward the Jacobian conjecture qsms 2021.05.28 2607
108 [QSMS Monthly Seminar] Symmetric functions and super duality qsms 2021.05.28 2165
107 [Seminar 2021.06.11] The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma qsms 2021.05.28 2131
106 [QSMS Monthly Seminar] Closed orbits and Beatty sequences qsms 2021.06.24 2173
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8