Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00209-003-0573-4
Title: On differential equations satisfied by modular forms
Authors: Yang, Y. 
Issue Date: Jan-2004
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
URI: http://scholarbank.nus.edu.sg/handle/10635/131458
ISSN: 00255874
DOI: 10.1007/s00209-003-0573-4
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