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https://doi.org/10.1007/s00209-003-0573-4
Title: | On differential equations satisfied by modular forms | Authors: | Yang, Y. | Issue Date: | Jan-2004 | Citation: | Yang, 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 | Abstract: | We 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. | Source Title: | Mathematische Zeitschrift | URI: | http://scholarbank.nus.edu.sg/handle/10635/131458 | ISSN: | 00255874 | DOI: | 10.1007/s00209-003-0573-4 |
Appears in Collections: | Staff Publications |
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