Differential equations satisfied by Eisenstein series of level 2

Toh, Pee Choon (2011) Differential equations satisfied by Eisenstein series of level 2. Ramanujan Journal, 25 2: 179-194. doi:10.1007/s11139-010-9242-5


Author Toh, Pee Choon
Title Differential equations satisfied by Eisenstein series of level 2
Journal name Ramanujan Journal   Check publisher's open access policy
ISSN 1382-4090
1572-9303
Publication date 2011-06-01
Sub-type Article (original research)
DOI 10.1007/s11139-010-9242-5
Open Access Status Not Open Access
Volume 25
Issue 2
Start page 179
End page 194
Total pages 16
Place of publication New York, NY, United States
Publisher Springer New York
Language eng
Subject 2602 Algebra and Number Theory
Formatted abstract
Ramanujan's differential equations for the classical Eisenstein series are of great importance to many areas in number theory and special functions. H. H. Chan recently demonstrated that these differential equations can be derived from the triple product identity and the quintuple product identity in an elementary manner. In this article, we extend this method in a uniform manner to derive corresponding differential equations for the Eisenstein series of level 2. Several applications of these differential equations are also given.
Keyword Eisenstein series
Jacobi theta functions
Differential equations
Triple product identity
Quintuple product identity
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 1 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Thu, 28 Nov 2013, 06:06:34 EST by System User on behalf of School of Mathematics & Physics