Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00209-003-0573-4
DC FieldValue
dc.titleOn differential equations satisfied by modular forms
dc.contributor.authorYang, Y.
dc.date.accessioned2016-11-28T10:20:28Z
dc.date.available2016-11-28T10:20:28Z
dc.date.issued2004-01
dc.identifier.citationYang, Y. (2004-01). On differential equations satisfied by modular forms. Mathematische Zeitschrift 246 (1-2) : 1-19. ScholarBank@NUS Repository. https://doi.org/10.1007/s00209-003-0573-4
dc.identifier.issn00255874
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/131458
dc.description.abstractWe use the theory of modular functions to give a new proof of a result of P. F. Stiller, which asserts that, if t is a non-constant meromorphic modular function of weight 0 and F is a meromorphic modular form of weight k with respect to a discrete subgroup of SL2(ℝ) commensurable with SL2(ℤ), then F, as a function of t, satisfies a (k + 1)-st order linear differential equation with algebraic functions of t as coefficients. Furthermore, we show that the Schwarzian differential equation for the modular function t can be extracted from any given (k + 1)-st order linear differential equation of this type. One advantage of our approach is that every coefficient in the differential equations can be relatively easily determined.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1007/s00209-003-0573-4
dc.sourceScopus
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1007/s00209-003-0573-4
dc.description.sourcetitleMathematische Zeitschrift
dc.description.volume246
dc.description.issue1-2
dc.description.page1-19
dc.identifier.isiut000187291700001
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