RISC JKU
  • @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 = {Schloss Hagenberg, 4232 Hagenberg, Austria}
    }