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|Title:||On differential equations satisfied by modular forms|
|Source:||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|
|Appears in Collections:||Staff Publications|
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