Please use this identifier to cite or link to this item:
|Title:||On differential equations satisfied by modular forms|
|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|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Nov 13, 2018
WEB OF SCIENCETM
checked on Oct 22, 2018
checked on Oct 11, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.