@techreport{RISC6109,author = {Peter Paule and Cristian-Silviu Radu},
title = {{An algorithm to prove holonomic differential equations for modular forms}},
language = {english},
abstract = {Express a modular form $g$ of positive weight
locally in terms of a modular function $h$ as
$y(h)$, say. Then $y(h)$ as a function in $h$ satisfies
a holonomic differential equation; i.e., one which is
linear with coefficients being polynomials in $h$.
This fact traces back to Gau{\ss} and has been
popularized prominently by Zagier. Using holonomic
procedures, computationally it is often straightforward
to derive such differential equations as conjectures.
In the spirit of the
``first guess, then prove'' paradigm,
we present a new algorithm to prove such conjectures.},
year = {2020},
month = {May},
keywords = {modular functions, modular forms, holonomic differential equations, holonomic functions and sequences, Fricke-Klein relations, $q$-series, partition congruences},
sponsor = {FWF SFB F50},
length = {48},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}