https://scholars.lib.ntu.edu.tw/handle/123456789/626608
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.author | Zhijie Chen | en_US |
dc.contributor.author | CHANG-SHOU LIN | en_US |
dc.contributor.author | YI-FAN YANG | en_US |
dc.date.accessioned | 2022-12-19T07:00:53Z | - |
dc.date.available | 2022-12-19T07:00:53Z | - |
dc.date.issued | 2022 | - |
dc.identifier.issn | 1815-0659 | - |
dc.identifier.uri | https://scholars.lib.ntu.edu.tw/handle/123456789/626608 | - |
dc.description.abstract | In this paper, we study third-order modular ordinary differential equations (MODE for short) of the following form $y'''+Q_2(z)y'+Q_3(z)y=0$, $z\in\mathbb{H}=\{z\in\mathbb{C} \,|\,\operatorname{Im}z>0 \}$, where $Q_2(z)$ and $Q_3(z)-\frac12 Q_2'(z)$ are meromorphic modular forms on ${\rm SL}(2,\mathbb{Z})$ of weight $4$ and $6$, respectively. We show that any quasimodular form of depth $2$ on ${\rm SL}(2,\mathbb{Z})$ leads to such a MODE. Conversely, we introduce the so-called Bol representation $\hat{\rho}\colon {\rm SL}(2,\mathbb{Z})\to{\rm SL}(3,\mathbb{C})$ for this MODE and give the necessary and sufficient condition for the irreducibility (resp. reducibility) of the representation. We show that the irreducibility yields the quasimodularity of some solution of this MODE, while the reducibility yields the modularity of all solutions and leads to solutions of certain ${\rm SU}(3)$ Toda systems. Note that the ${\rm SU}(N+1)$ Toda systems are the classical Pl\"ucker infinitesimal formulas for holomorphic maps from a Riemann surface to $\mathbb{CP}^N$. | en_US |
dc.publisher | NATL ACAD SCI UKRAINE, INST MATH | en_US |
dc.relation.ispartof | SIGMA 18 (2022), 013, 50 pages | en_US |
dc.subject | modular differential equations; quasimodular forms; Toda system; GENERALIZED LAME EQUATION; VERTEX OPERATOR-ALGEBRAS; FORMS; CLASSIFICATION; GEOMETRY; Mathematics - Number Theory; Mathematics - Number Theory | en_US |
dc.title | Modular Ordinary Differential Equations on ${\rm SL}(2,\mathbb{Z})$ of Third Order and Applications | en_US |
dc.type | journal article | en |
dc.identifier.doi | 10.3842/SIGMA.2022.013 | - |
dc.identifier.scopus | 2-s2.0-85127477607 | - |
dc.identifier.isi | WOS:000760346800001 | - |
dc.identifier.url | http://arxiv.org/abs/2106.12438v2 | - |
dc.relation.journalvolume | 18 | en_US |
item.openairetype | journal article | - |
item.openairecristype | http://purl.org/coar/resource_type/c_6501 | - |
item.cerifentitytype | Publications | - |
item.fulltext | no fulltext | - |
item.grantfulltext | none | - |
crisitem.author.dept | Mathematics | - |
crisitem.author.dept | Center for Advanced Study in Theoretical Sciences (CASTS) | - |
crisitem.author.dept | Mathematics | - |
crisitem.author.orcid | 0000-0001-7446-0251 | - |
crisitem.author.parentorg | College of Science | - |
crisitem.author.parentorg | Others: University-Level Research Centers | - |
crisitem.author.parentorg | College of Science | - |
顯示於: | 數學系 |
在 IR 系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。