Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jnt.2007.08.015
Title: Eisenstein series and theta functions to the septic base
Authors: Chan, H.H. 
Cooper, S.
Issue Date: Mar-2008
Citation: Chan, H.H., Cooper, S. (2008-03). Eisenstein series and theta functions to the septic base. Journal of Number Theory 128 (3) : 680-699. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jnt.2007.08.015
Abstract: We develop a theory for Eisenstein series to the septic base, which was started by S. Ramanujan in his "Lost Notebook." We show that two types of septic Eisenstein series may be parameterized in terms of the septic theta function ∑m = - ∞ ∞ ∑n = - ∞ ∞ qm2 + m n + 2 n2 and the eta quotient η4 (7 τ) / η4 (τ). This is accomplished by constructing elliptic functions which have the septic Eisenstein series as Taylor coefficients. The elliptic functions are shown to be solutions of a differential equation, and this leads to a recurrence relation for the septic Eisenstein series. © 2007 Elsevier Inc. All rights reserved.
Source Title: Journal of Number Theory
URI: http://scholarbank.nus.edu.sg/handle/10635/103194
ISSN: 0022314X
DOI: 10.1016/j.jnt.2007.08.015
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