On the sum of positive divisors functions

DOI10.1007/s40993-021-00240-6zbMath1478.11063OpenAlexW3135937390MaRDI QIDQ2020009

Radek Erban, Robert A. van Gorder

Publication date: 23 April 2021

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40993-021-00240-6

zbMATH Keywords

Eisenstein seriessingular equationsRamanujan differential equations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Holomorphic modular forms of integral weight (11F11) Arithmetic functions; related numbers; inversion formulas (11A25) Relations between ergodic theory and number theory (37A44)

Cites Work

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• Differential equations satisfied by Eisenstein series of level 2
• Evaluation of the convolution sums \(\sum _{l+6m=n}\sigma (l)\sigma (m)\) and \(\sum _{2l+3m=n}\sigma (l)\sigma (m)\)
• The hypergeometric equation and Ramanujan functions
• Basic representations for Eisenstein series from their differential equations
• Thetanulls and differential equations
• Eisenstein Series and Modular Differential Equations
• DIFFERENTIAL EQUATIONS FOR CUBIC THETA FUNCTIONS
• Triple product identity, Quintuple product identity and Ramanujan’s differential equations for the classical Eisenstein series
• Ramanujan’s convolution sum twisted by Dirichlet characters
• Solving Ramanujan's differential equations for Eisenstein series via a first order Riccati equation

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