Eisenstein series and their applications to some arithmetic identities and congruences

DOI10.1186/1687-1847-2013-84zbMath1380.11003OpenAlexW2165646349WikidataQ59293484 ScholiaQ59293484MaRDI QIDQ1693564

Aeran Kim, Ayyadurai Sankaranarayanan, Daeyeoul Kim

Publication date: 31 January 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2013-84

zbMATH Keywords

\(q\)-seriesEisenstein seriescongruence relationsconvolution sums\(q\)-productsdivisor functionsrestricted divisor functions

Mathematics Subject Classification ID

Arithmetic algebraic geometry (Diophantine geometry) (11G99) Congruences; primitive roots; residue systems (11A07) Arithmetic functions; related numbers; inversion formulas (11A25)

Cites Work

• The action of Hecke operators to families of Weierstrass-type functions and Weber-type functions and their applications
• The convolution sum \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\)
• Modular forms arising from divisor functions
• On the representation of integers as sums of triangular numbers
• Algebraic integers as values of elliptic functions
• A note on Bernoulli identities associated with the Weierstrass ℘-function
• Some families of Weierstrass-type functions and their applications
• Chapter 15 of Ramanujan's Second Notebook: Part 2, Modular forms
• CONVOLUTION SUMS ARISING FROM DIVISOR FUNCTIONS
• 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