Holonomic relations for modular functions and forms: First guess, then prove

DOI10.1142/S1793042120400278zbMath1475.11065OpenAlexW3089221236MaRDI QIDQ4991703

Paule, Peter, Cristian-Silviu Radu

Publication date: 3 June 2021

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042120400278

zbMATH Keywords

\(q\)-seriesmodular functionsmodular formspartition congruencesFricke-Klein relationsholonomic differential equationsholonomic functions and sequences

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) (q)-calculus and related topics (05A30) Partitions; congruences and congruential restrictions (11P83) Modular and automorphic functions (11F03) Congruences for modular and (p)-adic modular forms (11F33)

Related Items (2)

Interview with Peter Paule ⋮ An algorithm to prove holonomic differential equations for modular forms

Uses Software

• HolonomicFunctions
• GeneratingFunctions

Cites Work

• The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates
• A holonomic systems approach to special functions identities
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• On differential equations satisfied by modular forms
• Another congruence for the Apéry numbers
• On the computation of identities relating partition numbers in arithmetic progressions with eta quotients: an implementation of Radu's algorithm
• A proof of the Weierstraß gap theorem not using the Riemann-Roch formula
• Defining equations of modular curves
• Ramanujan's Theta Functions
• Elliptic Modular Forms and Their Applications
• Generalized Frobenius partitions
• Ramanujan's Lost Notebook
• Modular Forms
• Ramanujan's Lost Notebook
• Ramanujan's Lost Notebook
• Ramanujan's Lost Notebook
• Riemann surfaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Holonomic relations for modular functions and forms: First guess, then prove