Peter Paule, Silviu Radu,
"An algorithm to prove holonomic differential equations for modular forms"
, in Bostan A., Raschel K.: Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2019, Serie Springer Proceedings in Mathematics & Statistics, Vol. 373, Seite(n) 367-420, 2021, ISBN: 978-3-030-84303-8
Original Titel:
An algorithm to prove holonomic differential equations for modular forms
Sprache des Titels:
Englisch
Original Buchtitel:
Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2019
Original Kurzfassung:
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.