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.},
number = {20-05},
year = {2020},
month = {May},
note = {A final version appeared in: Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2029, eds.: A. Bostan and K. Raschel, Springer, 2021},
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 = {Schloss Hagenberg, 4232 Hagenberg, Austria}